Supercritical Water-Cooled Reactors Guest Editors: Jiejin Cai, Claude Renault, and Junli Gou Science and Technology of Nuclear Installations
Supercritical Water-Cooled Reactors
Guest Editors Jiejin Cai Claude Renault and Junli Gou
Science and Technology of Nuclear Installations
Supercritical Water-Cooled Reactors
Science and Technology of Nuclear Installations
Supercritical Water-Cooled Reactors
Guest Editors Jiejin Cai Claude Renault and Junli Gou
Copyright copy 2014 Hindawi Publishing Corporation All rights reserved
This is a special issue published in ldquoScience and Technology of Nuclear Installationsrdquo All articles are open access articles distributed underthe Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium providedthe original work is properly cited
Editorial Board
Nusret Aksan SwitzerlandA Alvim BrazilWon Pil Baek KoreaStephen M Bajorek USAGeorge Bakos GreeceJozsef Banati SwedenRicardo Barros BrazilAnis B Salah BelgiumGiovanni B Bruna FranceNikola Cavlina CroatiaXu Cheng ChinaLeon Cizelj SloveniaA Clausse ArgentinaFrancesco Drsquo Auria ItalyMarcos P de Abreu BrazilGiovanni DellrsquoOrco FranceJuan C Ferreri ArgentinaNikolay Fil RussiaCesare Frepoli USAGiorgio Galassi ItalyRegina Galetti Brazil
Michel Giot BelgiumValerio Giusti ItalyHorst Glaeser GermanySatish Kumar Gupta IndiaAli Hainoun SyriaKeith E Holbert USAKostadin Ivanov USAY Kadi Republic of KoreaAhmed Khedr EgyptTomasz Kozlowski USATomoaki Kunugi JapanMike Kuznetsov GermanyH-Y Lee Republic of KoreaB Limmeechokchai ThailandJiri Macek Czech RepublicAnnalisa Manera USABorut Mavko SloveniaOleg Melikhov RussiaRafael Miro SpainJOZEF Misak Czech RepublicRahim Nabbi Germany
Manmohan Pandey IndiaYuriy Parfenov RussiaYves Pontillon FranceNik Popov CanadaPiero Ravetto ItalyFrancesc Reventos SpainEnrico Sartori FranceCarlo Sborchia FranceMassimo Sepielli ItalyArkady Serikov GermanyJames F Stubbins USAIztok Tiselj SloveniaRizwan Uddin USAE Uspuras LithuaniaRichard Wright NorwayChao Xu ChinaX George Xu USAYanko Yanev BulgariaZhiwei Zhou ChinaEnrico Zio ItalyMassimo Zucchetti Italy
Contents
Supercritical Water-Cooled Reactors Jiejin Cai Claude Renault and Junli GouVolume 2014 Article ID 548672 2 pages
Core Flow Distribution from Coupled Supercritical Water Reactor Analysis Po Hu and Paul P H WilsonVolume 2014 Article ID 178129 8 pages
Code Development in Coupled PARCSRELAP5 for Supercritical Water Reactor Po Hu and Paul WilsonVolume 2014 Article ID 286434 8 pages
Preliminary Development ofThermal Power Calculation Code H-Power for a Supercritical WaterReactor Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao GuoVolume 2014 Article ID 279092 10 pages
A Simplified Supercritical Fast Reactor withThorium Fuel Peng Zhang Kan Wang and Ganglin YuVolume 2014 Article ID 405654 9 pages
Experimental Investigation on Flow-Induced Vibration of Fuel Rods in Supercritical Water LoopLicun Wu Daogang Lu and Yu LiuVolume 2014 Article ID 769432 9 pages
EditorialSupercritical Water-Cooled Reactors
Jiejin Cai1 Claude Renault2 and Junli Gou3
1 Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai Guangdong 519082 China2 INSTNPSNE The French Alternative Energies and Atomic Energy Commission (CEA) Saclay 91191 Gif-sur-Yvette France3 School of Nuclear Science and Technology Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China
Correspondence should be addressed to Jiejin Cai chiven77hotmailcom
Received 24 July 2014 Accepted 24 July 2014 Published 18 August 2014
Copyright copy 2014 Jiejin Cai et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Supercritical water-cooled reactor (SCWR) is the water-cooled reactor using supercritical pressure water as coolant[1] It is considered as one of the promising Generation IVreactors due to its advantages of plant simplification and highthermal efficiency [2 3]
Several design concepts of SCWRs have been proposed(a) supercritical water-cooled thermal neutron reactor (b)supercritical water-cooled fast neutron reactor (c) super-critical water-cooled mixed neutron spectrum reactor (d)supercritical water-cooled pebble bed reactor (e) supercrit-ical heavy-water-cooled reactor The detailed design param-eters of some typical SCWR concepts around the world aresummarized in Table 1 [4] Recently the use of thorium in theSCWRs has been investigated [5 6]
The advantages of the SCWRs are shown as follows [1](i) Supercritical water has excellent heat transfer proper-
ties allowing a high power density a small core and asmall containment structure
(ii) The use of a supercritical Rankine cycle with its typi-cally higher temperatures improves efficiency (wouldbe sim45)
(iii) This higher efficiency would lead to better fuel econ-omy and a lighter fuel load lessening residual (decay)heat
(iv) SCWR is typically designed as a once-through directcycle whereby steam or hot supercritical water fromthe core is used directly in a steam turbine whichmakes the design simple
(v) Water is liquid at room temperature cheap nontoxicand transparent simplifying inspection and repair(compared to liquid metal cooled reactors)
(vi) A fast SCWR could be a breeder reactor which couldburn the long-lived actinide isotopes
(vii) A heavy-water SCWR could breed fuel from thorium(4x more abundant than uranium) with increasedproliferation resistance over plutonium breeders
Some challenges in SCWRs are the subjects of researchwork which need us to research among which are thefollowing [4ndash7]
(i) Lower water inventory (due to compact primaryloop) means less heat capacity to buffer transientsand accidents (eg loss of feedwater flow or largebreak loss of coolant accident) resulting in accidentand transient temperatures that are too high forconventional metallic cladding
(ii) Higher pressure combined with higher temperatureand also a higher temperature rise across the coreresult in increased mechanical and thermal stresseson vessel materials that are difficult to solve
(iii) The coolant greatly reduces its density at the exit ofthe core resulting in a need to place extra moderatorthere
(iv) Extensive material development and research onsupercritical water chemistry under radiation areneeded
(v) Special start-up procedures are needed to avoid insta-bility before the water reaches supercritical condi-tions
(vi) A fast neutron SCWR requires a relatively complexreactor core design in order to achieve a negative voidcoefficient
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 548672 2 pageshttpdxdoiorg1011552014548672
2 Science and Technology of Nuclear Installations
Table 1 Some typical SCWR concepts around the world
Name Proposed by Design concept ModerateRatedpower(MW)
Outlettemperature
(∘C)
Pressure(MPa)
Net efficiency()
W21 Tokyo University Thermal neutronspectrum SCWR H2O 1570 508 25 44
TWG1 Water TWG (Japan) Fast neutronspectrum SCWR H2O 1728 Alternative Alternative 38sim45
W6-1
AECL (Canada)
CANDU-X-MARK1
D2O
910 430 25 41W6-2 CANDU-XNC 370 400 25 41W6-3 CANDU-ALX1 950 450 25 406W6-4 CANDU-X-ALX2 1143 650 25 45mdash Europe HPLWR H2O 1000 500 25 44
mdash INEL (USA) Thermal neutronspectrum SCWR H2O 1600 500 25 44
B500SKD1 Russia Integrative SCWR H2O 515 381 236 38
In order to help readers understand the development ofthe SCWRs in the world we sponsored a special issue onthe supercritical water-cooled reactor and hoped to get somepapers from the topics which include but are not limited tothe following
(i) reactor core and fuel designs(ii) materials chemistry and corrosion(iii) thermal-hydraulics and safety analysis(iv) plant systems structures and components(v) computational fluid dynamics (CFD) and coupled
codes(vi) neutronic properties(vii) balance of plant(viii) other applications
Now the special issue is published which includes 5papers The contents include a new concept of core designlike ldquoA simplified supercritical fast reactor with thorium fuelrdquocalculation code development like ldquoPreliminary developmentof thermal power calculation code H-power for a supercriticalwater reactorrdquo ldquoCode development in coupled PARCSRELAP5for supercritical water reactorrdquo and flow distribution one ofthe important issues of thermal hydraulics in the nuclearreactor like ldquoCore flow distribution from coupled supercriticalwater reactor analysisrdquo It also contains some experimen-tal results like ldquoExperimental investigation on flow-inducedvibration of fuel rods in supercritical water looprdquoWe hope thatreaders of this special issuewill find not only the developmentstatus of SCWRs and updated reviews on SCWRs but alsothe formulation of important questions to be resolved suchas how to develop the codes for SCWRs
Jiejin CaiClaude Renault
Junli Gou
References
[1] Y Oka S Koshizuka Y Ishiwatari and A Yamaji Super LightWater Reactors and Super Fast Reactors SpringerNewYorkNYUSA 2010
[2] S Liu and J Cai ldquoConvergence analysis of neutronicther-mohydraulic coupling behavior of SCWRrdquoNuclear Engineeringand Design vol 265 pp 53ndash62 2013
[3] S Liu and J Cai ldquoNeutronic and thermohydraulic character-istics of a new breeding thorium-uranium mixed SCWR fuelassemblyrdquo Annals of Nuclear Energy vol 62 no 1 pp 429ndash4362013
[4] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[5] S Liu and J Cai ldquoNeutronics assessment of thorium-based fuelassembly in SCWRrdquo Nuclear Engineering and Design vol 260pp 1ndash10 2013
[6] S Liu and J Cai ldquoDesign amp optimization of two breedingthorium-uranium mixed SCWR fuel assembliesrdquo Progress ofNuclear Energy vol 70 pp 6ndash19 2014
[7] Ph Marsault C Renault G Rimpault P Dumaz and OAntoni ldquoPre-design studies of SCWR in fast neutron spectrumevaluation of operating conditions and analysis of the behaviorin accidental situationsrdquo in Proceedings of the InternationalConference of Asian Political Parties (ICAPP rsquo04) Pittsburgh PaUSA June 2004
Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis
Po Hu1 and Paul P H Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal
1 Introduction
The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]
In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions
2 Analysis Methodology
21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]
To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]
Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 178129 8 pageshttpdxdoiorg1011552014178129
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Supercritical Water-Cooled Reactors
Science and Technology of Nuclear Installations
Supercritical Water-Cooled Reactors
Guest Editors Jiejin Cai Claude Renault and Junli Gou
Copyright copy 2014 Hindawi Publishing Corporation All rights reserved
This is a special issue published in ldquoScience and Technology of Nuclear Installationsrdquo All articles are open access articles distributed underthe Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium providedthe original work is properly cited
Editorial Board
Nusret Aksan SwitzerlandA Alvim BrazilWon Pil Baek KoreaStephen M Bajorek USAGeorge Bakos GreeceJozsef Banati SwedenRicardo Barros BrazilAnis B Salah BelgiumGiovanni B Bruna FranceNikola Cavlina CroatiaXu Cheng ChinaLeon Cizelj SloveniaA Clausse ArgentinaFrancesco Drsquo Auria ItalyMarcos P de Abreu BrazilGiovanni DellrsquoOrco FranceJuan C Ferreri ArgentinaNikolay Fil RussiaCesare Frepoli USAGiorgio Galassi ItalyRegina Galetti Brazil
Michel Giot BelgiumValerio Giusti ItalyHorst Glaeser GermanySatish Kumar Gupta IndiaAli Hainoun SyriaKeith E Holbert USAKostadin Ivanov USAY Kadi Republic of KoreaAhmed Khedr EgyptTomasz Kozlowski USATomoaki Kunugi JapanMike Kuznetsov GermanyH-Y Lee Republic of KoreaB Limmeechokchai ThailandJiri Macek Czech RepublicAnnalisa Manera USABorut Mavko SloveniaOleg Melikhov RussiaRafael Miro SpainJOZEF Misak Czech RepublicRahim Nabbi Germany
Manmohan Pandey IndiaYuriy Parfenov RussiaYves Pontillon FranceNik Popov CanadaPiero Ravetto ItalyFrancesc Reventos SpainEnrico Sartori FranceCarlo Sborchia FranceMassimo Sepielli ItalyArkady Serikov GermanyJames F Stubbins USAIztok Tiselj SloveniaRizwan Uddin USAE Uspuras LithuaniaRichard Wright NorwayChao Xu ChinaX George Xu USAYanko Yanev BulgariaZhiwei Zhou ChinaEnrico Zio ItalyMassimo Zucchetti Italy
Contents
Supercritical Water-Cooled Reactors Jiejin Cai Claude Renault and Junli GouVolume 2014 Article ID 548672 2 pages
Core Flow Distribution from Coupled Supercritical Water Reactor Analysis Po Hu and Paul P H WilsonVolume 2014 Article ID 178129 8 pages
Code Development in Coupled PARCSRELAP5 for Supercritical Water Reactor Po Hu and Paul WilsonVolume 2014 Article ID 286434 8 pages
Preliminary Development ofThermal Power Calculation Code H-Power for a Supercritical WaterReactor Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao GuoVolume 2014 Article ID 279092 10 pages
A Simplified Supercritical Fast Reactor withThorium Fuel Peng Zhang Kan Wang and Ganglin YuVolume 2014 Article ID 405654 9 pages
Experimental Investigation on Flow-Induced Vibration of Fuel Rods in Supercritical Water LoopLicun Wu Daogang Lu and Yu LiuVolume 2014 Article ID 769432 9 pages
EditorialSupercritical Water-Cooled Reactors
Jiejin Cai1 Claude Renault2 and Junli Gou3
1 Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai Guangdong 519082 China2 INSTNPSNE The French Alternative Energies and Atomic Energy Commission (CEA) Saclay 91191 Gif-sur-Yvette France3 School of Nuclear Science and Technology Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China
Correspondence should be addressed to Jiejin Cai chiven77hotmailcom
Received 24 July 2014 Accepted 24 July 2014 Published 18 August 2014
Copyright copy 2014 Jiejin Cai et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Supercritical water-cooled reactor (SCWR) is the water-cooled reactor using supercritical pressure water as coolant[1] It is considered as one of the promising Generation IVreactors due to its advantages of plant simplification and highthermal efficiency [2 3]
Several design concepts of SCWRs have been proposed(a) supercritical water-cooled thermal neutron reactor (b)supercritical water-cooled fast neutron reactor (c) super-critical water-cooled mixed neutron spectrum reactor (d)supercritical water-cooled pebble bed reactor (e) supercrit-ical heavy-water-cooled reactor The detailed design param-eters of some typical SCWR concepts around the world aresummarized in Table 1 [4] Recently the use of thorium in theSCWRs has been investigated [5 6]
The advantages of the SCWRs are shown as follows [1](i) Supercritical water has excellent heat transfer proper-
ties allowing a high power density a small core and asmall containment structure
(ii) The use of a supercritical Rankine cycle with its typi-cally higher temperatures improves efficiency (wouldbe sim45)
(iii) This higher efficiency would lead to better fuel econ-omy and a lighter fuel load lessening residual (decay)heat
(iv) SCWR is typically designed as a once-through directcycle whereby steam or hot supercritical water fromthe core is used directly in a steam turbine whichmakes the design simple
(v) Water is liquid at room temperature cheap nontoxicand transparent simplifying inspection and repair(compared to liquid metal cooled reactors)
(vi) A fast SCWR could be a breeder reactor which couldburn the long-lived actinide isotopes
(vii) A heavy-water SCWR could breed fuel from thorium(4x more abundant than uranium) with increasedproliferation resistance over plutonium breeders
Some challenges in SCWRs are the subjects of researchwork which need us to research among which are thefollowing [4ndash7]
(i) Lower water inventory (due to compact primaryloop) means less heat capacity to buffer transientsand accidents (eg loss of feedwater flow or largebreak loss of coolant accident) resulting in accidentand transient temperatures that are too high forconventional metallic cladding
(ii) Higher pressure combined with higher temperatureand also a higher temperature rise across the coreresult in increased mechanical and thermal stresseson vessel materials that are difficult to solve
(iii) The coolant greatly reduces its density at the exit ofthe core resulting in a need to place extra moderatorthere
(iv) Extensive material development and research onsupercritical water chemistry under radiation areneeded
(v) Special start-up procedures are needed to avoid insta-bility before the water reaches supercritical condi-tions
(vi) A fast neutron SCWR requires a relatively complexreactor core design in order to achieve a negative voidcoefficient
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 548672 2 pageshttpdxdoiorg1011552014548672
2 Science and Technology of Nuclear Installations
Table 1 Some typical SCWR concepts around the world
Name Proposed by Design concept ModerateRatedpower(MW)
Outlettemperature
(∘C)
Pressure(MPa)
Net efficiency()
W21 Tokyo University Thermal neutronspectrum SCWR H2O 1570 508 25 44
TWG1 Water TWG (Japan) Fast neutronspectrum SCWR H2O 1728 Alternative Alternative 38sim45
W6-1
AECL (Canada)
CANDU-X-MARK1
D2O
910 430 25 41W6-2 CANDU-XNC 370 400 25 41W6-3 CANDU-ALX1 950 450 25 406W6-4 CANDU-X-ALX2 1143 650 25 45mdash Europe HPLWR H2O 1000 500 25 44
mdash INEL (USA) Thermal neutronspectrum SCWR H2O 1600 500 25 44
B500SKD1 Russia Integrative SCWR H2O 515 381 236 38
In order to help readers understand the development ofthe SCWRs in the world we sponsored a special issue onthe supercritical water-cooled reactor and hoped to get somepapers from the topics which include but are not limited tothe following
(i) reactor core and fuel designs(ii) materials chemistry and corrosion(iii) thermal-hydraulics and safety analysis(iv) plant systems structures and components(v) computational fluid dynamics (CFD) and coupled
codes(vi) neutronic properties(vii) balance of plant(viii) other applications
Now the special issue is published which includes 5papers The contents include a new concept of core designlike ldquoA simplified supercritical fast reactor with thorium fuelrdquocalculation code development like ldquoPreliminary developmentof thermal power calculation code H-power for a supercriticalwater reactorrdquo ldquoCode development in coupled PARCSRELAP5for supercritical water reactorrdquo and flow distribution one ofthe important issues of thermal hydraulics in the nuclearreactor like ldquoCore flow distribution from coupled supercriticalwater reactor analysisrdquo It also contains some experimen-tal results like ldquoExperimental investigation on flow-inducedvibration of fuel rods in supercritical water looprdquoWe hope thatreaders of this special issuewill find not only the developmentstatus of SCWRs and updated reviews on SCWRs but alsothe formulation of important questions to be resolved suchas how to develop the codes for SCWRs
Jiejin CaiClaude Renault
Junli Gou
References
[1] Y Oka S Koshizuka Y Ishiwatari and A Yamaji Super LightWater Reactors and Super Fast Reactors SpringerNewYorkNYUSA 2010
[2] S Liu and J Cai ldquoConvergence analysis of neutronicther-mohydraulic coupling behavior of SCWRrdquoNuclear Engineeringand Design vol 265 pp 53ndash62 2013
[3] S Liu and J Cai ldquoNeutronic and thermohydraulic character-istics of a new breeding thorium-uranium mixed SCWR fuelassemblyrdquo Annals of Nuclear Energy vol 62 no 1 pp 429ndash4362013
[4] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[5] S Liu and J Cai ldquoNeutronics assessment of thorium-based fuelassembly in SCWRrdquo Nuclear Engineering and Design vol 260pp 1ndash10 2013
[6] S Liu and J Cai ldquoDesign amp optimization of two breedingthorium-uranium mixed SCWR fuel assembliesrdquo Progress ofNuclear Energy vol 70 pp 6ndash19 2014
[7] Ph Marsault C Renault G Rimpault P Dumaz and OAntoni ldquoPre-design studies of SCWR in fast neutron spectrumevaluation of operating conditions and analysis of the behaviorin accidental situationsrdquo in Proceedings of the InternationalConference of Asian Political Parties (ICAPP rsquo04) Pittsburgh PaUSA June 2004
Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis
Po Hu1 and Paul P H Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal
1 Introduction
The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]
In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions
2 Analysis Methodology
21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]
To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]
Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 178129 8 pageshttpdxdoiorg1011552014178129
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations
Supercritical Water-Cooled Reactors
Guest Editors Jiejin Cai Claude Renault and Junli Gou
Copyright copy 2014 Hindawi Publishing Corporation All rights reserved
This is a special issue published in ldquoScience and Technology of Nuclear Installationsrdquo All articles are open access articles distributed underthe Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium providedthe original work is properly cited
Editorial Board
Nusret Aksan SwitzerlandA Alvim BrazilWon Pil Baek KoreaStephen M Bajorek USAGeorge Bakos GreeceJozsef Banati SwedenRicardo Barros BrazilAnis B Salah BelgiumGiovanni B Bruna FranceNikola Cavlina CroatiaXu Cheng ChinaLeon Cizelj SloveniaA Clausse ArgentinaFrancesco Drsquo Auria ItalyMarcos P de Abreu BrazilGiovanni DellrsquoOrco FranceJuan C Ferreri ArgentinaNikolay Fil RussiaCesare Frepoli USAGiorgio Galassi ItalyRegina Galetti Brazil
Michel Giot BelgiumValerio Giusti ItalyHorst Glaeser GermanySatish Kumar Gupta IndiaAli Hainoun SyriaKeith E Holbert USAKostadin Ivanov USAY Kadi Republic of KoreaAhmed Khedr EgyptTomasz Kozlowski USATomoaki Kunugi JapanMike Kuznetsov GermanyH-Y Lee Republic of KoreaB Limmeechokchai ThailandJiri Macek Czech RepublicAnnalisa Manera USABorut Mavko SloveniaOleg Melikhov RussiaRafael Miro SpainJOZEF Misak Czech RepublicRahim Nabbi Germany
Manmohan Pandey IndiaYuriy Parfenov RussiaYves Pontillon FranceNik Popov CanadaPiero Ravetto ItalyFrancesc Reventos SpainEnrico Sartori FranceCarlo Sborchia FranceMassimo Sepielli ItalyArkady Serikov GermanyJames F Stubbins USAIztok Tiselj SloveniaRizwan Uddin USAE Uspuras LithuaniaRichard Wright NorwayChao Xu ChinaX George Xu USAYanko Yanev BulgariaZhiwei Zhou ChinaEnrico Zio ItalyMassimo Zucchetti Italy
Contents
Supercritical Water-Cooled Reactors Jiejin Cai Claude Renault and Junli GouVolume 2014 Article ID 548672 2 pages
Core Flow Distribution from Coupled Supercritical Water Reactor Analysis Po Hu and Paul P H WilsonVolume 2014 Article ID 178129 8 pages
Code Development in Coupled PARCSRELAP5 for Supercritical Water Reactor Po Hu and Paul WilsonVolume 2014 Article ID 286434 8 pages
Preliminary Development ofThermal Power Calculation Code H-Power for a Supercritical WaterReactor Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao GuoVolume 2014 Article ID 279092 10 pages
A Simplified Supercritical Fast Reactor withThorium Fuel Peng Zhang Kan Wang and Ganglin YuVolume 2014 Article ID 405654 9 pages
Experimental Investigation on Flow-Induced Vibration of Fuel Rods in Supercritical Water LoopLicun Wu Daogang Lu and Yu LiuVolume 2014 Article ID 769432 9 pages
EditorialSupercritical Water-Cooled Reactors
Jiejin Cai1 Claude Renault2 and Junli Gou3
1 Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai Guangdong 519082 China2 INSTNPSNE The French Alternative Energies and Atomic Energy Commission (CEA) Saclay 91191 Gif-sur-Yvette France3 School of Nuclear Science and Technology Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China
Correspondence should be addressed to Jiejin Cai chiven77hotmailcom
Received 24 July 2014 Accepted 24 July 2014 Published 18 August 2014
Copyright copy 2014 Jiejin Cai et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Supercritical water-cooled reactor (SCWR) is the water-cooled reactor using supercritical pressure water as coolant[1] It is considered as one of the promising Generation IVreactors due to its advantages of plant simplification and highthermal efficiency [2 3]
Several design concepts of SCWRs have been proposed(a) supercritical water-cooled thermal neutron reactor (b)supercritical water-cooled fast neutron reactor (c) super-critical water-cooled mixed neutron spectrum reactor (d)supercritical water-cooled pebble bed reactor (e) supercrit-ical heavy-water-cooled reactor The detailed design param-eters of some typical SCWR concepts around the world aresummarized in Table 1 [4] Recently the use of thorium in theSCWRs has been investigated [5 6]
The advantages of the SCWRs are shown as follows [1](i) Supercritical water has excellent heat transfer proper-
ties allowing a high power density a small core and asmall containment structure
(ii) The use of a supercritical Rankine cycle with its typi-cally higher temperatures improves efficiency (wouldbe sim45)
(iii) This higher efficiency would lead to better fuel econ-omy and a lighter fuel load lessening residual (decay)heat
(iv) SCWR is typically designed as a once-through directcycle whereby steam or hot supercritical water fromthe core is used directly in a steam turbine whichmakes the design simple
(v) Water is liquid at room temperature cheap nontoxicand transparent simplifying inspection and repair(compared to liquid metal cooled reactors)
(vi) A fast SCWR could be a breeder reactor which couldburn the long-lived actinide isotopes
(vii) A heavy-water SCWR could breed fuel from thorium(4x more abundant than uranium) with increasedproliferation resistance over plutonium breeders
Some challenges in SCWRs are the subjects of researchwork which need us to research among which are thefollowing [4ndash7]
(i) Lower water inventory (due to compact primaryloop) means less heat capacity to buffer transientsand accidents (eg loss of feedwater flow or largebreak loss of coolant accident) resulting in accidentand transient temperatures that are too high forconventional metallic cladding
(ii) Higher pressure combined with higher temperatureand also a higher temperature rise across the coreresult in increased mechanical and thermal stresseson vessel materials that are difficult to solve
(iii) The coolant greatly reduces its density at the exit ofthe core resulting in a need to place extra moderatorthere
(iv) Extensive material development and research onsupercritical water chemistry under radiation areneeded
(v) Special start-up procedures are needed to avoid insta-bility before the water reaches supercritical condi-tions
(vi) A fast neutron SCWR requires a relatively complexreactor core design in order to achieve a negative voidcoefficient
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 548672 2 pageshttpdxdoiorg1011552014548672
2 Science and Technology of Nuclear Installations
Table 1 Some typical SCWR concepts around the world
Name Proposed by Design concept ModerateRatedpower(MW)
Outlettemperature
(∘C)
Pressure(MPa)
Net efficiency()
W21 Tokyo University Thermal neutronspectrum SCWR H2O 1570 508 25 44
TWG1 Water TWG (Japan) Fast neutronspectrum SCWR H2O 1728 Alternative Alternative 38sim45
W6-1
AECL (Canada)
CANDU-X-MARK1
D2O
910 430 25 41W6-2 CANDU-XNC 370 400 25 41W6-3 CANDU-ALX1 950 450 25 406W6-4 CANDU-X-ALX2 1143 650 25 45mdash Europe HPLWR H2O 1000 500 25 44
mdash INEL (USA) Thermal neutronspectrum SCWR H2O 1600 500 25 44
B500SKD1 Russia Integrative SCWR H2O 515 381 236 38
In order to help readers understand the development ofthe SCWRs in the world we sponsored a special issue onthe supercritical water-cooled reactor and hoped to get somepapers from the topics which include but are not limited tothe following
(i) reactor core and fuel designs(ii) materials chemistry and corrosion(iii) thermal-hydraulics and safety analysis(iv) plant systems structures and components(v) computational fluid dynamics (CFD) and coupled
codes(vi) neutronic properties(vii) balance of plant(viii) other applications
Now the special issue is published which includes 5papers The contents include a new concept of core designlike ldquoA simplified supercritical fast reactor with thorium fuelrdquocalculation code development like ldquoPreliminary developmentof thermal power calculation code H-power for a supercriticalwater reactorrdquo ldquoCode development in coupled PARCSRELAP5for supercritical water reactorrdquo and flow distribution one ofthe important issues of thermal hydraulics in the nuclearreactor like ldquoCore flow distribution from coupled supercriticalwater reactor analysisrdquo It also contains some experimen-tal results like ldquoExperimental investigation on flow-inducedvibration of fuel rods in supercritical water looprdquoWe hope thatreaders of this special issuewill find not only the developmentstatus of SCWRs and updated reviews on SCWRs but alsothe formulation of important questions to be resolved suchas how to develop the codes for SCWRs
Jiejin CaiClaude Renault
Junli Gou
References
[1] Y Oka S Koshizuka Y Ishiwatari and A Yamaji Super LightWater Reactors and Super Fast Reactors SpringerNewYorkNYUSA 2010
[2] S Liu and J Cai ldquoConvergence analysis of neutronicther-mohydraulic coupling behavior of SCWRrdquoNuclear Engineeringand Design vol 265 pp 53ndash62 2013
[3] S Liu and J Cai ldquoNeutronic and thermohydraulic character-istics of a new breeding thorium-uranium mixed SCWR fuelassemblyrdquo Annals of Nuclear Energy vol 62 no 1 pp 429ndash4362013
[4] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[5] S Liu and J Cai ldquoNeutronics assessment of thorium-based fuelassembly in SCWRrdquo Nuclear Engineering and Design vol 260pp 1ndash10 2013
[6] S Liu and J Cai ldquoDesign amp optimization of two breedingthorium-uranium mixed SCWR fuel assembliesrdquo Progress ofNuclear Energy vol 70 pp 6ndash19 2014
[7] Ph Marsault C Renault G Rimpault P Dumaz and OAntoni ldquoPre-design studies of SCWR in fast neutron spectrumevaluation of operating conditions and analysis of the behaviorin accidental situationsrdquo in Proceedings of the InternationalConference of Asian Political Parties (ICAPP rsquo04) Pittsburgh PaUSA June 2004
Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis
Po Hu1 and Paul P H Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal
1 Introduction
The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]
In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions
2 Analysis Methodology
21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]
To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]
Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 178129 8 pageshttpdxdoiorg1011552014178129
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Copyright copy 2014 Hindawi Publishing Corporation All rights reserved
This is a special issue published in ldquoScience and Technology of Nuclear Installationsrdquo All articles are open access articles distributed underthe Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium providedthe original work is properly cited
Editorial Board
Nusret Aksan SwitzerlandA Alvim BrazilWon Pil Baek KoreaStephen M Bajorek USAGeorge Bakos GreeceJozsef Banati SwedenRicardo Barros BrazilAnis B Salah BelgiumGiovanni B Bruna FranceNikola Cavlina CroatiaXu Cheng ChinaLeon Cizelj SloveniaA Clausse ArgentinaFrancesco Drsquo Auria ItalyMarcos P de Abreu BrazilGiovanni DellrsquoOrco FranceJuan C Ferreri ArgentinaNikolay Fil RussiaCesare Frepoli USAGiorgio Galassi ItalyRegina Galetti Brazil
Michel Giot BelgiumValerio Giusti ItalyHorst Glaeser GermanySatish Kumar Gupta IndiaAli Hainoun SyriaKeith E Holbert USAKostadin Ivanov USAY Kadi Republic of KoreaAhmed Khedr EgyptTomasz Kozlowski USATomoaki Kunugi JapanMike Kuznetsov GermanyH-Y Lee Republic of KoreaB Limmeechokchai ThailandJiri Macek Czech RepublicAnnalisa Manera USABorut Mavko SloveniaOleg Melikhov RussiaRafael Miro SpainJOZEF Misak Czech RepublicRahim Nabbi Germany
Manmohan Pandey IndiaYuriy Parfenov RussiaYves Pontillon FranceNik Popov CanadaPiero Ravetto ItalyFrancesc Reventos SpainEnrico Sartori FranceCarlo Sborchia FranceMassimo Sepielli ItalyArkady Serikov GermanyJames F Stubbins USAIztok Tiselj SloveniaRizwan Uddin USAE Uspuras LithuaniaRichard Wright NorwayChao Xu ChinaX George Xu USAYanko Yanev BulgariaZhiwei Zhou ChinaEnrico Zio ItalyMassimo Zucchetti Italy
Contents
Supercritical Water-Cooled Reactors Jiejin Cai Claude Renault and Junli GouVolume 2014 Article ID 548672 2 pages
Core Flow Distribution from Coupled Supercritical Water Reactor Analysis Po Hu and Paul P H WilsonVolume 2014 Article ID 178129 8 pages
Code Development in Coupled PARCSRELAP5 for Supercritical Water Reactor Po Hu and Paul WilsonVolume 2014 Article ID 286434 8 pages
Preliminary Development ofThermal Power Calculation Code H-Power for a Supercritical WaterReactor Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao GuoVolume 2014 Article ID 279092 10 pages
A Simplified Supercritical Fast Reactor withThorium Fuel Peng Zhang Kan Wang and Ganglin YuVolume 2014 Article ID 405654 9 pages
Experimental Investigation on Flow-Induced Vibration of Fuel Rods in Supercritical Water LoopLicun Wu Daogang Lu and Yu LiuVolume 2014 Article ID 769432 9 pages
EditorialSupercritical Water-Cooled Reactors
Jiejin Cai1 Claude Renault2 and Junli Gou3
1 Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai Guangdong 519082 China2 INSTNPSNE The French Alternative Energies and Atomic Energy Commission (CEA) Saclay 91191 Gif-sur-Yvette France3 School of Nuclear Science and Technology Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China
Correspondence should be addressed to Jiejin Cai chiven77hotmailcom
Received 24 July 2014 Accepted 24 July 2014 Published 18 August 2014
Copyright copy 2014 Jiejin Cai et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Supercritical water-cooled reactor (SCWR) is the water-cooled reactor using supercritical pressure water as coolant[1] It is considered as one of the promising Generation IVreactors due to its advantages of plant simplification and highthermal efficiency [2 3]
Several design concepts of SCWRs have been proposed(a) supercritical water-cooled thermal neutron reactor (b)supercritical water-cooled fast neutron reactor (c) super-critical water-cooled mixed neutron spectrum reactor (d)supercritical water-cooled pebble bed reactor (e) supercrit-ical heavy-water-cooled reactor The detailed design param-eters of some typical SCWR concepts around the world aresummarized in Table 1 [4] Recently the use of thorium in theSCWRs has been investigated [5 6]
The advantages of the SCWRs are shown as follows [1](i) Supercritical water has excellent heat transfer proper-
ties allowing a high power density a small core and asmall containment structure
(ii) The use of a supercritical Rankine cycle with its typi-cally higher temperatures improves efficiency (wouldbe sim45)
(iii) This higher efficiency would lead to better fuel econ-omy and a lighter fuel load lessening residual (decay)heat
(iv) SCWR is typically designed as a once-through directcycle whereby steam or hot supercritical water fromthe core is used directly in a steam turbine whichmakes the design simple
(v) Water is liquid at room temperature cheap nontoxicand transparent simplifying inspection and repair(compared to liquid metal cooled reactors)
(vi) A fast SCWR could be a breeder reactor which couldburn the long-lived actinide isotopes
(vii) A heavy-water SCWR could breed fuel from thorium(4x more abundant than uranium) with increasedproliferation resistance over plutonium breeders
Some challenges in SCWRs are the subjects of researchwork which need us to research among which are thefollowing [4ndash7]
(i) Lower water inventory (due to compact primaryloop) means less heat capacity to buffer transientsand accidents (eg loss of feedwater flow or largebreak loss of coolant accident) resulting in accidentand transient temperatures that are too high forconventional metallic cladding
(ii) Higher pressure combined with higher temperatureand also a higher temperature rise across the coreresult in increased mechanical and thermal stresseson vessel materials that are difficult to solve
(iii) The coolant greatly reduces its density at the exit ofthe core resulting in a need to place extra moderatorthere
(iv) Extensive material development and research onsupercritical water chemistry under radiation areneeded
(v) Special start-up procedures are needed to avoid insta-bility before the water reaches supercritical condi-tions
(vi) A fast neutron SCWR requires a relatively complexreactor core design in order to achieve a negative voidcoefficient
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 548672 2 pageshttpdxdoiorg1011552014548672
2 Science and Technology of Nuclear Installations
Table 1 Some typical SCWR concepts around the world
Name Proposed by Design concept ModerateRatedpower(MW)
Outlettemperature
(∘C)
Pressure(MPa)
Net efficiency()
W21 Tokyo University Thermal neutronspectrum SCWR H2O 1570 508 25 44
TWG1 Water TWG (Japan) Fast neutronspectrum SCWR H2O 1728 Alternative Alternative 38sim45
W6-1
AECL (Canada)
CANDU-X-MARK1
D2O
910 430 25 41W6-2 CANDU-XNC 370 400 25 41W6-3 CANDU-ALX1 950 450 25 406W6-4 CANDU-X-ALX2 1143 650 25 45mdash Europe HPLWR H2O 1000 500 25 44
mdash INEL (USA) Thermal neutronspectrum SCWR H2O 1600 500 25 44
B500SKD1 Russia Integrative SCWR H2O 515 381 236 38
In order to help readers understand the development ofthe SCWRs in the world we sponsored a special issue onthe supercritical water-cooled reactor and hoped to get somepapers from the topics which include but are not limited tothe following
(i) reactor core and fuel designs(ii) materials chemistry and corrosion(iii) thermal-hydraulics and safety analysis(iv) plant systems structures and components(v) computational fluid dynamics (CFD) and coupled
codes(vi) neutronic properties(vii) balance of plant(viii) other applications
Now the special issue is published which includes 5papers The contents include a new concept of core designlike ldquoA simplified supercritical fast reactor with thorium fuelrdquocalculation code development like ldquoPreliminary developmentof thermal power calculation code H-power for a supercriticalwater reactorrdquo ldquoCode development in coupled PARCSRELAP5for supercritical water reactorrdquo and flow distribution one ofthe important issues of thermal hydraulics in the nuclearreactor like ldquoCore flow distribution from coupled supercriticalwater reactor analysisrdquo It also contains some experimen-tal results like ldquoExperimental investigation on flow-inducedvibration of fuel rods in supercritical water looprdquoWe hope thatreaders of this special issuewill find not only the developmentstatus of SCWRs and updated reviews on SCWRs but alsothe formulation of important questions to be resolved suchas how to develop the codes for SCWRs
Jiejin CaiClaude Renault
Junli Gou
References
[1] Y Oka S Koshizuka Y Ishiwatari and A Yamaji Super LightWater Reactors and Super Fast Reactors SpringerNewYorkNYUSA 2010
[2] S Liu and J Cai ldquoConvergence analysis of neutronicther-mohydraulic coupling behavior of SCWRrdquoNuclear Engineeringand Design vol 265 pp 53ndash62 2013
[3] S Liu and J Cai ldquoNeutronic and thermohydraulic character-istics of a new breeding thorium-uranium mixed SCWR fuelassemblyrdquo Annals of Nuclear Energy vol 62 no 1 pp 429ndash4362013
[4] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[5] S Liu and J Cai ldquoNeutronics assessment of thorium-based fuelassembly in SCWRrdquo Nuclear Engineering and Design vol 260pp 1ndash10 2013
[6] S Liu and J Cai ldquoDesign amp optimization of two breedingthorium-uranium mixed SCWR fuel assembliesrdquo Progress ofNuclear Energy vol 70 pp 6ndash19 2014
[7] Ph Marsault C Renault G Rimpault P Dumaz and OAntoni ldquoPre-design studies of SCWR in fast neutron spectrumevaluation of operating conditions and analysis of the behaviorin accidental situationsrdquo in Proceedings of the InternationalConference of Asian Political Parties (ICAPP rsquo04) Pittsburgh PaUSA June 2004
Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis
Po Hu1 and Paul P H Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal
1 Introduction
The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]
In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions
2 Analysis Methodology
21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]
To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]
Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 178129 8 pageshttpdxdoiorg1011552014178129
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Editorial Board
Nusret Aksan SwitzerlandA Alvim BrazilWon Pil Baek KoreaStephen M Bajorek USAGeorge Bakos GreeceJozsef Banati SwedenRicardo Barros BrazilAnis B Salah BelgiumGiovanni B Bruna FranceNikola Cavlina CroatiaXu Cheng ChinaLeon Cizelj SloveniaA Clausse ArgentinaFrancesco Drsquo Auria ItalyMarcos P de Abreu BrazilGiovanni DellrsquoOrco FranceJuan C Ferreri ArgentinaNikolay Fil RussiaCesare Frepoli USAGiorgio Galassi ItalyRegina Galetti Brazil
Michel Giot BelgiumValerio Giusti ItalyHorst Glaeser GermanySatish Kumar Gupta IndiaAli Hainoun SyriaKeith E Holbert USAKostadin Ivanov USAY Kadi Republic of KoreaAhmed Khedr EgyptTomasz Kozlowski USATomoaki Kunugi JapanMike Kuznetsov GermanyH-Y Lee Republic of KoreaB Limmeechokchai ThailandJiri Macek Czech RepublicAnnalisa Manera USABorut Mavko SloveniaOleg Melikhov RussiaRafael Miro SpainJOZEF Misak Czech RepublicRahim Nabbi Germany
Manmohan Pandey IndiaYuriy Parfenov RussiaYves Pontillon FranceNik Popov CanadaPiero Ravetto ItalyFrancesc Reventos SpainEnrico Sartori FranceCarlo Sborchia FranceMassimo Sepielli ItalyArkady Serikov GermanyJames F Stubbins USAIztok Tiselj SloveniaRizwan Uddin USAE Uspuras LithuaniaRichard Wright NorwayChao Xu ChinaX George Xu USAYanko Yanev BulgariaZhiwei Zhou ChinaEnrico Zio ItalyMassimo Zucchetti Italy
Contents
Supercritical Water-Cooled Reactors Jiejin Cai Claude Renault and Junli GouVolume 2014 Article ID 548672 2 pages
Core Flow Distribution from Coupled Supercritical Water Reactor Analysis Po Hu and Paul P H WilsonVolume 2014 Article ID 178129 8 pages
Code Development in Coupled PARCSRELAP5 for Supercritical Water Reactor Po Hu and Paul WilsonVolume 2014 Article ID 286434 8 pages
Preliminary Development ofThermal Power Calculation Code H-Power for a Supercritical WaterReactor Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao GuoVolume 2014 Article ID 279092 10 pages
A Simplified Supercritical Fast Reactor withThorium Fuel Peng Zhang Kan Wang and Ganglin YuVolume 2014 Article ID 405654 9 pages
Experimental Investigation on Flow-Induced Vibration of Fuel Rods in Supercritical Water LoopLicun Wu Daogang Lu and Yu LiuVolume 2014 Article ID 769432 9 pages
EditorialSupercritical Water-Cooled Reactors
Jiejin Cai1 Claude Renault2 and Junli Gou3
1 Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai Guangdong 519082 China2 INSTNPSNE The French Alternative Energies and Atomic Energy Commission (CEA) Saclay 91191 Gif-sur-Yvette France3 School of Nuclear Science and Technology Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China
Correspondence should be addressed to Jiejin Cai chiven77hotmailcom
Received 24 July 2014 Accepted 24 July 2014 Published 18 August 2014
Copyright copy 2014 Jiejin Cai et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Supercritical water-cooled reactor (SCWR) is the water-cooled reactor using supercritical pressure water as coolant[1] It is considered as one of the promising Generation IVreactors due to its advantages of plant simplification and highthermal efficiency [2 3]
Several design concepts of SCWRs have been proposed(a) supercritical water-cooled thermal neutron reactor (b)supercritical water-cooled fast neutron reactor (c) super-critical water-cooled mixed neutron spectrum reactor (d)supercritical water-cooled pebble bed reactor (e) supercrit-ical heavy-water-cooled reactor The detailed design param-eters of some typical SCWR concepts around the world aresummarized in Table 1 [4] Recently the use of thorium in theSCWRs has been investigated [5 6]
The advantages of the SCWRs are shown as follows [1](i) Supercritical water has excellent heat transfer proper-
ties allowing a high power density a small core and asmall containment structure
(ii) The use of a supercritical Rankine cycle with its typi-cally higher temperatures improves efficiency (wouldbe sim45)
(iii) This higher efficiency would lead to better fuel econ-omy and a lighter fuel load lessening residual (decay)heat
(iv) SCWR is typically designed as a once-through directcycle whereby steam or hot supercritical water fromthe core is used directly in a steam turbine whichmakes the design simple
(v) Water is liquid at room temperature cheap nontoxicand transparent simplifying inspection and repair(compared to liquid metal cooled reactors)
(vi) A fast SCWR could be a breeder reactor which couldburn the long-lived actinide isotopes
(vii) A heavy-water SCWR could breed fuel from thorium(4x more abundant than uranium) with increasedproliferation resistance over plutonium breeders
Some challenges in SCWRs are the subjects of researchwork which need us to research among which are thefollowing [4ndash7]
(i) Lower water inventory (due to compact primaryloop) means less heat capacity to buffer transientsand accidents (eg loss of feedwater flow or largebreak loss of coolant accident) resulting in accidentand transient temperatures that are too high forconventional metallic cladding
(ii) Higher pressure combined with higher temperatureand also a higher temperature rise across the coreresult in increased mechanical and thermal stresseson vessel materials that are difficult to solve
(iii) The coolant greatly reduces its density at the exit ofthe core resulting in a need to place extra moderatorthere
(iv) Extensive material development and research onsupercritical water chemistry under radiation areneeded
(v) Special start-up procedures are needed to avoid insta-bility before the water reaches supercritical condi-tions
(vi) A fast neutron SCWR requires a relatively complexreactor core design in order to achieve a negative voidcoefficient
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 548672 2 pageshttpdxdoiorg1011552014548672
2 Science and Technology of Nuclear Installations
Table 1 Some typical SCWR concepts around the world
Name Proposed by Design concept ModerateRatedpower(MW)
Outlettemperature
(∘C)
Pressure(MPa)
Net efficiency()
W21 Tokyo University Thermal neutronspectrum SCWR H2O 1570 508 25 44
TWG1 Water TWG (Japan) Fast neutronspectrum SCWR H2O 1728 Alternative Alternative 38sim45
W6-1
AECL (Canada)
CANDU-X-MARK1
D2O
910 430 25 41W6-2 CANDU-XNC 370 400 25 41W6-3 CANDU-ALX1 950 450 25 406W6-4 CANDU-X-ALX2 1143 650 25 45mdash Europe HPLWR H2O 1000 500 25 44
mdash INEL (USA) Thermal neutronspectrum SCWR H2O 1600 500 25 44
B500SKD1 Russia Integrative SCWR H2O 515 381 236 38
In order to help readers understand the development ofthe SCWRs in the world we sponsored a special issue onthe supercritical water-cooled reactor and hoped to get somepapers from the topics which include but are not limited tothe following
(i) reactor core and fuel designs(ii) materials chemistry and corrosion(iii) thermal-hydraulics and safety analysis(iv) plant systems structures and components(v) computational fluid dynamics (CFD) and coupled
codes(vi) neutronic properties(vii) balance of plant(viii) other applications
Now the special issue is published which includes 5papers The contents include a new concept of core designlike ldquoA simplified supercritical fast reactor with thorium fuelrdquocalculation code development like ldquoPreliminary developmentof thermal power calculation code H-power for a supercriticalwater reactorrdquo ldquoCode development in coupled PARCSRELAP5for supercritical water reactorrdquo and flow distribution one ofthe important issues of thermal hydraulics in the nuclearreactor like ldquoCore flow distribution from coupled supercriticalwater reactor analysisrdquo It also contains some experimen-tal results like ldquoExperimental investigation on flow-inducedvibration of fuel rods in supercritical water looprdquoWe hope thatreaders of this special issuewill find not only the developmentstatus of SCWRs and updated reviews on SCWRs but alsothe formulation of important questions to be resolved suchas how to develop the codes for SCWRs
Jiejin CaiClaude Renault
Junli Gou
References
[1] Y Oka S Koshizuka Y Ishiwatari and A Yamaji Super LightWater Reactors and Super Fast Reactors SpringerNewYorkNYUSA 2010
[2] S Liu and J Cai ldquoConvergence analysis of neutronicther-mohydraulic coupling behavior of SCWRrdquoNuclear Engineeringand Design vol 265 pp 53ndash62 2013
[3] S Liu and J Cai ldquoNeutronic and thermohydraulic character-istics of a new breeding thorium-uranium mixed SCWR fuelassemblyrdquo Annals of Nuclear Energy vol 62 no 1 pp 429ndash4362013
[4] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[5] S Liu and J Cai ldquoNeutronics assessment of thorium-based fuelassembly in SCWRrdquo Nuclear Engineering and Design vol 260pp 1ndash10 2013
[6] S Liu and J Cai ldquoDesign amp optimization of two breedingthorium-uranium mixed SCWR fuel assembliesrdquo Progress ofNuclear Energy vol 70 pp 6ndash19 2014
[7] Ph Marsault C Renault G Rimpault P Dumaz and OAntoni ldquoPre-design studies of SCWR in fast neutron spectrumevaluation of operating conditions and analysis of the behaviorin accidental situationsrdquo in Proceedings of the InternationalConference of Asian Political Parties (ICAPP rsquo04) Pittsburgh PaUSA June 2004
Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis
Po Hu1 and Paul P H Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal
1 Introduction
The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]
In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions
2 Analysis Methodology
21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]
To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]
Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 178129 8 pageshttpdxdoiorg1011552014178129
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Contents
Supercritical Water-Cooled Reactors Jiejin Cai Claude Renault and Junli GouVolume 2014 Article ID 548672 2 pages
Core Flow Distribution from Coupled Supercritical Water Reactor Analysis Po Hu and Paul P H WilsonVolume 2014 Article ID 178129 8 pages
Code Development in Coupled PARCSRELAP5 for Supercritical Water Reactor Po Hu and Paul WilsonVolume 2014 Article ID 286434 8 pages
Preliminary Development ofThermal Power Calculation Code H-Power for a Supercritical WaterReactor Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao GuoVolume 2014 Article ID 279092 10 pages
A Simplified Supercritical Fast Reactor withThorium Fuel Peng Zhang Kan Wang and Ganglin YuVolume 2014 Article ID 405654 9 pages
Experimental Investigation on Flow-Induced Vibration of Fuel Rods in Supercritical Water LoopLicun Wu Daogang Lu and Yu LiuVolume 2014 Article ID 769432 9 pages
EditorialSupercritical Water-Cooled Reactors
Jiejin Cai1 Claude Renault2 and Junli Gou3
1 Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai Guangdong 519082 China2 INSTNPSNE The French Alternative Energies and Atomic Energy Commission (CEA) Saclay 91191 Gif-sur-Yvette France3 School of Nuclear Science and Technology Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China
Correspondence should be addressed to Jiejin Cai chiven77hotmailcom
Received 24 July 2014 Accepted 24 July 2014 Published 18 August 2014
Copyright copy 2014 Jiejin Cai et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Supercritical water-cooled reactor (SCWR) is the water-cooled reactor using supercritical pressure water as coolant[1] It is considered as one of the promising Generation IVreactors due to its advantages of plant simplification and highthermal efficiency [2 3]
Several design concepts of SCWRs have been proposed(a) supercritical water-cooled thermal neutron reactor (b)supercritical water-cooled fast neutron reactor (c) super-critical water-cooled mixed neutron spectrum reactor (d)supercritical water-cooled pebble bed reactor (e) supercrit-ical heavy-water-cooled reactor The detailed design param-eters of some typical SCWR concepts around the world aresummarized in Table 1 [4] Recently the use of thorium in theSCWRs has been investigated [5 6]
The advantages of the SCWRs are shown as follows [1](i) Supercritical water has excellent heat transfer proper-
ties allowing a high power density a small core and asmall containment structure
(ii) The use of a supercritical Rankine cycle with its typi-cally higher temperatures improves efficiency (wouldbe sim45)
(iii) This higher efficiency would lead to better fuel econ-omy and a lighter fuel load lessening residual (decay)heat
(iv) SCWR is typically designed as a once-through directcycle whereby steam or hot supercritical water fromthe core is used directly in a steam turbine whichmakes the design simple
(v) Water is liquid at room temperature cheap nontoxicand transparent simplifying inspection and repair(compared to liquid metal cooled reactors)
(vi) A fast SCWR could be a breeder reactor which couldburn the long-lived actinide isotopes
(vii) A heavy-water SCWR could breed fuel from thorium(4x more abundant than uranium) with increasedproliferation resistance over plutonium breeders
Some challenges in SCWRs are the subjects of researchwork which need us to research among which are thefollowing [4ndash7]
(i) Lower water inventory (due to compact primaryloop) means less heat capacity to buffer transientsand accidents (eg loss of feedwater flow or largebreak loss of coolant accident) resulting in accidentand transient temperatures that are too high forconventional metallic cladding
(ii) Higher pressure combined with higher temperatureand also a higher temperature rise across the coreresult in increased mechanical and thermal stresseson vessel materials that are difficult to solve
(iii) The coolant greatly reduces its density at the exit ofthe core resulting in a need to place extra moderatorthere
(iv) Extensive material development and research onsupercritical water chemistry under radiation areneeded
(v) Special start-up procedures are needed to avoid insta-bility before the water reaches supercritical condi-tions
(vi) A fast neutron SCWR requires a relatively complexreactor core design in order to achieve a negative voidcoefficient
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 548672 2 pageshttpdxdoiorg1011552014548672
2 Science and Technology of Nuclear Installations
Table 1 Some typical SCWR concepts around the world
Name Proposed by Design concept ModerateRatedpower(MW)
Outlettemperature
(∘C)
Pressure(MPa)
Net efficiency()
W21 Tokyo University Thermal neutronspectrum SCWR H2O 1570 508 25 44
TWG1 Water TWG (Japan) Fast neutronspectrum SCWR H2O 1728 Alternative Alternative 38sim45
W6-1
AECL (Canada)
CANDU-X-MARK1
D2O
910 430 25 41W6-2 CANDU-XNC 370 400 25 41W6-3 CANDU-ALX1 950 450 25 406W6-4 CANDU-X-ALX2 1143 650 25 45mdash Europe HPLWR H2O 1000 500 25 44
mdash INEL (USA) Thermal neutronspectrum SCWR H2O 1600 500 25 44
B500SKD1 Russia Integrative SCWR H2O 515 381 236 38
In order to help readers understand the development ofthe SCWRs in the world we sponsored a special issue onthe supercritical water-cooled reactor and hoped to get somepapers from the topics which include but are not limited tothe following
(i) reactor core and fuel designs(ii) materials chemistry and corrosion(iii) thermal-hydraulics and safety analysis(iv) plant systems structures and components(v) computational fluid dynamics (CFD) and coupled
codes(vi) neutronic properties(vii) balance of plant(viii) other applications
Now the special issue is published which includes 5papers The contents include a new concept of core designlike ldquoA simplified supercritical fast reactor with thorium fuelrdquocalculation code development like ldquoPreliminary developmentof thermal power calculation code H-power for a supercriticalwater reactorrdquo ldquoCode development in coupled PARCSRELAP5for supercritical water reactorrdquo and flow distribution one ofthe important issues of thermal hydraulics in the nuclearreactor like ldquoCore flow distribution from coupled supercriticalwater reactor analysisrdquo It also contains some experimen-tal results like ldquoExperimental investigation on flow-inducedvibration of fuel rods in supercritical water looprdquoWe hope thatreaders of this special issuewill find not only the developmentstatus of SCWRs and updated reviews on SCWRs but alsothe formulation of important questions to be resolved suchas how to develop the codes for SCWRs
Jiejin CaiClaude Renault
Junli Gou
References
[1] Y Oka S Koshizuka Y Ishiwatari and A Yamaji Super LightWater Reactors and Super Fast Reactors SpringerNewYorkNYUSA 2010
[2] S Liu and J Cai ldquoConvergence analysis of neutronicther-mohydraulic coupling behavior of SCWRrdquoNuclear Engineeringand Design vol 265 pp 53ndash62 2013
[3] S Liu and J Cai ldquoNeutronic and thermohydraulic character-istics of a new breeding thorium-uranium mixed SCWR fuelassemblyrdquo Annals of Nuclear Energy vol 62 no 1 pp 429ndash4362013
[4] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[5] S Liu and J Cai ldquoNeutronics assessment of thorium-based fuelassembly in SCWRrdquo Nuclear Engineering and Design vol 260pp 1ndash10 2013
[6] S Liu and J Cai ldquoDesign amp optimization of two breedingthorium-uranium mixed SCWR fuel assembliesrdquo Progress ofNuclear Energy vol 70 pp 6ndash19 2014
[7] Ph Marsault C Renault G Rimpault P Dumaz and OAntoni ldquoPre-design studies of SCWR in fast neutron spectrumevaluation of operating conditions and analysis of the behaviorin accidental situationsrdquo in Proceedings of the InternationalConference of Asian Political Parties (ICAPP rsquo04) Pittsburgh PaUSA June 2004
Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis
Po Hu1 and Paul P H Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal
1 Introduction
The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]
In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions
2 Analysis Methodology
21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]
To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]
Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 178129 8 pageshttpdxdoiorg1011552014178129
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
EditorialSupercritical Water-Cooled Reactors
Jiejin Cai1 Claude Renault2 and Junli Gou3
1 Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai Guangdong 519082 China2 INSTNPSNE The French Alternative Energies and Atomic Energy Commission (CEA) Saclay 91191 Gif-sur-Yvette France3 School of Nuclear Science and Technology Xirsquoan Jiaotong University Xirsquoan Shaanxi 710049 China
Correspondence should be addressed to Jiejin Cai chiven77hotmailcom
Received 24 July 2014 Accepted 24 July 2014 Published 18 August 2014
Copyright copy 2014 Jiejin Cai et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Supercritical water-cooled reactor (SCWR) is the water-cooled reactor using supercritical pressure water as coolant[1] It is considered as one of the promising Generation IVreactors due to its advantages of plant simplification and highthermal efficiency [2 3]
Several design concepts of SCWRs have been proposed(a) supercritical water-cooled thermal neutron reactor (b)supercritical water-cooled fast neutron reactor (c) super-critical water-cooled mixed neutron spectrum reactor (d)supercritical water-cooled pebble bed reactor (e) supercrit-ical heavy-water-cooled reactor The detailed design param-eters of some typical SCWR concepts around the world aresummarized in Table 1 [4] Recently the use of thorium in theSCWRs has been investigated [5 6]
The advantages of the SCWRs are shown as follows [1](i) Supercritical water has excellent heat transfer proper-
ties allowing a high power density a small core and asmall containment structure
(ii) The use of a supercritical Rankine cycle with its typi-cally higher temperatures improves efficiency (wouldbe sim45)
(iii) This higher efficiency would lead to better fuel econ-omy and a lighter fuel load lessening residual (decay)heat
(iv) SCWR is typically designed as a once-through directcycle whereby steam or hot supercritical water fromthe core is used directly in a steam turbine whichmakes the design simple
(v) Water is liquid at room temperature cheap nontoxicand transparent simplifying inspection and repair(compared to liquid metal cooled reactors)
(vi) A fast SCWR could be a breeder reactor which couldburn the long-lived actinide isotopes
(vii) A heavy-water SCWR could breed fuel from thorium(4x more abundant than uranium) with increasedproliferation resistance over plutonium breeders
Some challenges in SCWRs are the subjects of researchwork which need us to research among which are thefollowing [4ndash7]
(i) Lower water inventory (due to compact primaryloop) means less heat capacity to buffer transientsand accidents (eg loss of feedwater flow or largebreak loss of coolant accident) resulting in accidentand transient temperatures that are too high forconventional metallic cladding
(ii) Higher pressure combined with higher temperatureand also a higher temperature rise across the coreresult in increased mechanical and thermal stresseson vessel materials that are difficult to solve
(iii) The coolant greatly reduces its density at the exit ofthe core resulting in a need to place extra moderatorthere
(iv) Extensive material development and research onsupercritical water chemistry under radiation areneeded
(v) Special start-up procedures are needed to avoid insta-bility before the water reaches supercritical condi-tions
(vi) A fast neutron SCWR requires a relatively complexreactor core design in order to achieve a negative voidcoefficient
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 548672 2 pageshttpdxdoiorg1011552014548672
2 Science and Technology of Nuclear Installations
Table 1 Some typical SCWR concepts around the world
Name Proposed by Design concept ModerateRatedpower(MW)
Outlettemperature
(∘C)
Pressure(MPa)
Net efficiency()
W21 Tokyo University Thermal neutronspectrum SCWR H2O 1570 508 25 44
TWG1 Water TWG (Japan) Fast neutronspectrum SCWR H2O 1728 Alternative Alternative 38sim45
W6-1
AECL (Canada)
CANDU-X-MARK1
D2O
910 430 25 41W6-2 CANDU-XNC 370 400 25 41W6-3 CANDU-ALX1 950 450 25 406W6-4 CANDU-X-ALX2 1143 650 25 45mdash Europe HPLWR H2O 1000 500 25 44
mdash INEL (USA) Thermal neutronspectrum SCWR H2O 1600 500 25 44
B500SKD1 Russia Integrative SCWR H2O 515 381 236 38
In order to help readers understand the development ofthe SCWRs in the world we sponsored a special issue onthe supercritical water-cooled reactor and hoped to get somepapers from the topics which include but are not limited tothe following
(i) reactor core and fuel designs(ii) materials chemistry and corrosion(iii) thermal-hydraulics and safety analysis(iv) plant systems structures and components(v) computational fluid dynamics (CFD) and coupled
codes(vi) neutronic properties(vii) balance of plant(viii) other applications
Now the special issue is published which includes 5papers The contents include a new concept of core designlike ldquoA simplified supercritical fast reactor with thorium fuelrdquocalculation code development like ldquoPreliminary developmentof thermal power calculation code H-power for a supercriticalwater reactorrdquo ldquoCode development in coupled PARCSRELAP5for supercritical water reactorrdquo and flow distribution one ofthe important issues of thermal hydraulics in the nuclearreactor like ldquoCore flow distribution from coupled supercriticalwater reactor analysisrdquo It also contains some experimen-tal results like ldquoExperimental investigation on flow-inducedvibration of fuel rods in supercritical water looprdquoWe hope thatreaders of this special issuewill find not only the developmentstatus of SCWRs and updated reviews on SCWRs but alsothe formulation of important questions to be resolved suchas how to develop the codes for SCWRs
Jiejin CaiClaude Renault
Junli Gou
References
[1] Y Oka S Koshizuka Y Ishiwatari and A Yamaji Super LightWater Reactors and Super Fast Reactors SpringerNewYorkNYUSA 2010
[2] S Liu and J Cai ldquoConvergence analysis of neutronicther-mohydraulic coupling behavior of SCWRrdquoNuclear Engineeringand Design vol 265 pp 53ndash62 2013
[3] S Liu and J Cai ldquoNeutronic and thermohydraulic character-istics of a new breeding thorium-uranium mixed SCWR fuelassemblyrdquo Annals of Nuclear Energy vol 62 no 1 pp 429ndash4362013
[4] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[5] S Liu and J Cai ldquoNeutronics assessment of thorium-based fuelassembly in SCWRrdquo Nuclear Engineering and Design vol 260pp 1ndash10 2013
[6] S Liu and J Cai ldquoDesign amp optimization of two breedingthorium-uranium mixed SCWR fuel assembliesrdquo Progress ofNuclear Energy vol 70 pp 6ndash19 2014
[7] Ph Marsault C Renault G Rimpault P Dumaz and OAntoni ldquoPre-design studies of SCWR in fast neutron spectrumevaluation of operating conditions and analysis of the behaviorin accidental situationsrdquo in Proceedings of the InternationalConference of Asian Political Parties (ICAPP rsquo04) Pittsburgh PaUSA June 2004
Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis
Po Hu1 and Paul P H Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal
1 Introduction
The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]
In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions
2 Analysis Methodology
21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]
To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]
Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 178129 8 pageshttpdxdoiorg1011552014178129
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
2 Science and Technology of Nuclear Installations
Table 1 Some typical SCWR concepts around the world
Name Proposed by Design concept ModerateRatedpower(MW)
Outlettemperature
(∘C)
Pressure(MPa)
Net efficiency()
W21 Tokyo University Thermal neutronspectrum SCWR H2O 1570 508 25 44
TWG1 Water TWG (Japan) Fast neutronspectrum SCWR H2O 1728 Alternative Alternative 38sim45
W6-1
AECL (Canada)
CANDU-X-MARK1
D2O
910 430 25 41W6-2 CANDU-XNC 370 400 25 41W6-3 CANDU-ALX1 950 450 25 406W6-4 CANDU-X-ALX2 1143 650 25 45mdash Europe HPLWR H2O 1000 500 25 44
mdash INEL (USA) Thermal neutronspectrum SCWR H2O 1600 500 25 44
B500SKD1 Russia Integrative SCWR H2O 515 381 236 38
In order to help readers understand the development ofthe SCWRs in the world we sponsored a special issue onthe supercritical water-cooled reactor and hoped to get somepapers from the topics which include but are not limited tothe following
(i) reactor core and fuel designs(ii) materials chemistry and corrosion(iii) thermal-hydraulics and safety analysis(iv) plant systems structures and components(v) computational fluid dynamics (CFD) and coupled
codes(vi) neutronic properties(vii) balance of plant(viii) other applications
Now the special issue is published which includes 5papers The contents include a new concept of core designlike ldquoA simplified supercritical fast reactor with thorium fuelrdquocalculation code development like ldquoPreliminary developmentof thermal power calculation code H-power for a supercriticalwater reactorrdquo ldquoCode development in coupled PARCSRELAP5for supercritical water reactorrdquo and flow distribution one ofthe important issues of thermal hydraulics in the nuclearreactor like ldquoCore flow distribution from coupled supercriticalwater reactor analysisrdquo It also contains some experimen-tal results like ldquoExperimental investigation on flow-inducedvibration of fuel rods in supercritical water looprdquoWe hope thatreaders of this special issuewill find not only the developmentstatus of SCWRs and updated reviews on SCWRs but alsothe formulation of important questions to be resolved suchas how to develop the codes for SCWRs
Jiejin CaiClaude Renault
Junli Gou
References
[1] Y Oka S Koshizuka Y Ishiwatari and A Yamaji Super LightWater Reactors and Super Fast Reactors SpringerNewYorkNYUSA 2010
[2] S Liu and J Cai ldquoConvergence analysis of neutronicther-mohydraulic coupling behavior of SCWRrdquoNuclear Engineeringand Design vol 265 pp 53ndash62 2013
[3] S Liu and J Cai ldquoNeutronic and thermohydraulic character-istics of a new breeding thorium-uranium mixed SCWR fuelassemblyrdquo Annals of Nuclear Energy vol 62 no 1 pp 429ndash4362013
[4] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[5] S Liu and J Cai ldquoNeutronics assessment of thorium-based fuelassembly in SCWRrdquo Nuclear Engineering and Design vol 260pp 1ndash10 2013
[6] S Liu and J Cai ldquoDesign amp optimization of two breedingthorium-uranium mixed SCWR fuel assembliesrdquo Progress ofNuclear Energy vol 70 pp 6ndash19 2014
[7] Ph Marsault C Renault G Rimpault P Dumaz and OAntoni ldquoPre-design studies of SCWR in fast neutron spectrumevaluation of operating conditions and analysis of the behaviorin accidental situationsrdquo in Proceedings of the InternationalConference of Asian Political Parties (ICAPP rsquo04) Pittsburgh PaUSA June 2004
Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis
Po Hu1 and Paul P H Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal
1 Introduction
The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]
In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions
2 Analysis Methodology
21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]
To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]
Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 178129 8 pageshttpdxdoiorg1011552014178129
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Research ArticleCore Flow Distribution from Coupled Supercritical WaterReactor Analysis
Po Hu1 and Paul P H Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 15 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P PHWilson This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper introduces an extended code package PARCSRELAP5 to analyze steady state of SCWR US reference design An 8 times8 quarter core model in PARCS and a reactor core model in RELAP5 are used to study the core flow distribution under varioussteady state conditions The possibility of moderator flow reversal is found in some hot moderator channels Different moderatorflow orifice strategies both uniform across the core and nonuniform based on the power distribution are explored with the goalof preventing the reversal
1 Introduction
The supercritical water reactor (SCWR) is a next generationnuclear reactor concept It is essentially a light water reactor(LWR) operating at higher pressure and temperature with adirect cycle Its higher thermal efficiency and considerableplant simplification have distinguished it from the currentreactors Oka and his team presented both a thermal and fastSCWR design [1 2] and Buongiorno presented a thermalSCWRas theUS reference design [3] andKim et al andXu etal presented various mixed spectrum (thermalfast) SCWRdesigns [4 5]
In the US reference SCWR design the majority of thecoolant firstly flows downward as a dedicated moderatorin separated water rods and then flows upward adjacentto the fuel pins as coolant Because of the large change inwater density through the pseudocritical point heat transferbetween the coolant and the moderator has an importantimpact in accurate SCWR reactor analysis This paper usesan extended code package which couples the core simulatorPARCS to the thermal-hydraulics simulator RELAP5 toanalyze both steady state and transient of SCWR design An8 times 8 quarter core model in PARCS and a reactor core modelin RELAP5 [6] are used to study the core flow distributionunder various steady state conditions
2 Analysis Methodology
21 Extended Code Package PARCS is a 3D core simulatorusing the nodal method to solve diffusion equation It isable to analyze PWR and BWR designs in which wateris used as both coolant and moderator in a single flowchannel In this work PARCS was modified to accommodatethermal-hydraulic feedback to the nuclear cross-sections ofthe separated coolant and moderator channels in SCWR Inaddition changes have been made to the communicationbetween PARCS andRELAP5 to accommodate these separateflows [7]
To enable the feedback from separated moderator a newsubroutine is added to look up macroscopichomogenizedcross-section information based on three thermal hydraulicproperties fuel temperature coolant density and moderatordensity The homogenized cross-section data is prepared bythe lattice transport code HELIOS [8]
Coupled PARCS and RELAP5 use lookup files to shareinformation between corresponding computational units(nodes for PARCS hydrodynamic volumes and heat struc-tures for RELAP5) In the original lookup file the nodesin PARCS correspond to the hydrodynamic volumes repre-senting the single fluid and the heat structures representing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 178129 8 pageshttpdxdoiorg1011552014178129
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
2 Science and Technology of Nuclear Installations
Water rod (times36)Fuel rod (times300)
Instrumentation pin
Control rod (times16)
Fuel assembly (1352MWdkgU)Fuel assembly ( 776MWdkgU)Full assembly (0001MWdkgU)Reflector
A1 B C D E F G
2
3
4
5
6
7
Figure 1 Fuel assembly and quarter core assembly arrangement
fuel cladding and other core structure components in twoseparate tables After the modification there are three tablesin the lookupfile one representing the coolant hydrodynamicvolumes one representing the moderator channel hydrody-namic volumes and one representing the heat structures
22 Core Models An 8times8 quarter core model is used inPARCS as show in Figure 1 with water reflectors at lateralboundaries and reflective boundary condition at top andbottom of the core The fuel arrangement shown in Figure 1is used in all the following calculationsThese particular bur-nupswere chosen to give an indication of the effect of burnupa real equilibrium core loading would have larger burnupsfor partially used fuel After considerations for symmetry the37 fuel assemblies in the PARCS model are coupled to 21unique flow paths in the RELAP5 model Both the PARCSand RELAP5 models have 12 axial nodes through the coreFlow paths in downcomer moderator upper plenum coreand lower plenum are modeled in RELAP5 A schematicof the flow path is shown in Figure 2 a moderator channeland a coolant channel represent one assembly in the coreIn addition to being in contact with the fuel heat structurethe coolant channel is thermally coupled to the moderatorchannel through another heat structure representing themoderator channel wall The majority of the inlet flow (90)to the core flows up to the moderator upper plenum and
FlowHeat
Moderator upper plenum
Coolant upper plenum
Dow
ncom
er
Lower plenum
Coolantchannels
Moderatorchannels
Figure 2 Flow pattern in RELAP5
then flows downward through moderator channels Nextall the moderator flow mixes with the downcomer flowand finally flows upwards through coolant channels andthe coolant upper plenum and to the outlet of vessel Thedesign parameters are shown in Table 1 Previous research
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 3
Table 1 SCWR nominal design parameters (Buongiorno et al 2003 [3])
Fuel pin CoreFuel material UO2 Thermal power 3575MWFissile enrichment 5 Number of fuel assemblies 148Fuel radius 0436 cm Active height 427mCladding material Stainless steel Effective diameter 393mCladding thickness 0063 cm Volumetric power density 69MWm3
Fuel pitch 112 cm Average linear heat rate 192 kWmPD 112
Fuel assembly Thermal-hydraulic parametersNumber of fuel rods 300 System pressure 25MPaNumber of water rods 36 Coolant flow rate 1843 kgsNumber of control rods 16 Moderator bypass 120573 10 (184 kgs)Assembly pitch 286 cm Inlet temperature 280∘CWater rod width 336 cm Outlet temperature 500∘CWater rod wall thickness 004 cm Thermal efficiency 4480
Table 2 Moderator flow rate and assembly power in the reference case
Flow rate (kgs) minus156 minus136 minus152 minus137 minus157 minus155 minus171Power (MW) 252 277 257 273 248 253 182Flow rate (kgs) minus136 minus75 minus131 36 minus136 minus137 minus172Power (MW) 277 268 278 248 274 274 161Flow rate (kgs) minus152 minus131 minus148 minus129 minus114 minus165Power (MW) 257 278 263 279 283 225Flow rate (kgs) minus137 36 minus129 minus104 minus156 minus172Power (MW) 273 248 2791 282 250 166Flow rate (kgs) minus157 minus136 minus114 minus156 minus171Power (MW) 248 274 283 250 179Flow rate (kgs) minus155 minus137 minus165 minus172Power (MW) 253 274 225 166Flow rate (kgs) minus171 minus172Power (MW) 182 161
[9] showed that the heat transfer between the coolant andmoderator channels could reduce the axial power peak bychanging the equivalent moderator density which representscombined moderation from moderator and coolant Theseresults were generated with a thermal hydraulic model insidePARCS assuming a fixed flow distribution in both moderatorand coolant channelsThis paper studies flow distributions insteady state using coupled PARCSRELAP5 The possibilityof moderator flow reversal is found in some hot moderatorchannels Different moderator flow orifice strategies bothuniform across the core and nonuniform based on the powerdistribution are explored with the goal of preventing thereversal
3 Reference Case
The reference model uses a uniform orifice size for eachmoderator flow channel with a ratio of the orifice area to themoderator area of 020 This results in flow reversal in somemoderator channels as shown in Table 2 Negative flow rates
indicate a downward flow as intended These results showthat two assemblies have reverse flow
31 Pressure Balance in Moderator Channel Due to buoy-ancy the flow rate in hotmoderator channels is lower than theflow rate in colder moderator channels Inmost of moderatorchannels a stable downward flow occurs as designated Inthe highest power channels due to the large density changethrough the pseudocritical point the buoyancy effect is solarge that the stable flow can be changed to flowupwardsThiscan result in a stable core flow distribution in which the flowin few moderator channels is upward while the flow in therest of moderator channels is downward
A reactor core designed with downward moderator flowmay not behave well when the flow reverses as unexpectedreversed channels will have power peak at the bottom forboth moderator and coolant that are flowing upwards andtheir densities are decreasing accordingly and these peaksmay be difficult to deal with during the depletion consideringthe control rods withdrawing from the top of the core and
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
4 Science and Technology of Nuclear Installations
0
2 4 6
1234567
0
061
081
102
2 4 6
2 4 6
1
2
3
4
5
6
7100
200
300
400
500
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
1021234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1
2
3
4
5
6
70
061
081
102
2 4 6
1
2
3
4
5
6
70
200
400
600
2 4 6
1
2
3
4
5
6
7
Moderator flow rate (kgs) Normalized assembly power
minus156 minus136
minus136
minus152 minus137 minus157 minus155 minus171
minus136 minus75 minus131 36 minus137 minus172
minus152 minus131 minus149 minus129 minus114 minus165
minus137 36 minus129 minus104 minus156 minus172
minus157 minus136 minus114 minus156 minus171
minus155 minus137 minus165 minus172
minus171 minus172minus15
minus10
minus5
0
minus15
minus10
minus5
0
minus15
minus10
minus5
r = 020
r = 018
r = 015
523 476 513 477 525 519 583
476 373 466 310 475 477 595
513 466 502 461 433 552
477 310 461 415 523 592
525 475 433 523 585
519 477 552 592
582 595
Equivalent density (kgm3)
Equivalent density (kgm3)
Equivalent density (kgm3)
105 116 107 114 103 105 076
116 112 116 104 114 115 067
067
107 116 110 117 118 094
114 104 117 118 105 069
103 114 118 105 075
105 115 094 069
076
103 115 107 115 102 103 073
115 117 117 115 115 114 065
107 117 110 118 119 092
115 115 118 119 103 067
102 115 119 113 073
103 114 092 067
073065
525 486 524 487 537 532 593
486 392 473 388 485 490 604
524 473 512 469 444 564
487 388 469 427 535 601
537 485 444 535 595
532 490 564 601
593 604
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
minus147 minus130 minus144 minus130 minus148 minus147 minus159
minus130 minus86 minus125 minus85 minus130 minus132 minus160
minus144 minus125 minus140 minus123 minus112 minus155
minus130 minus85 minus123 minus104 minus148 minus160
minus148 minus130 minus112 minus148 minus160
minus147 minus132 minus155 minus160
minus159minus160
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071063
Figure 3 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in different orifice area ratio119903 = 119860
119900
119860mod
the flow reversal may vanish over the cycle Therefore itis important to study the circumstances under which thisreversal occurs Furthermore there are at least two waysto manageprevent the moderator flow reversal A thermal-hydraulics approach based on flow orifices in the moderatorchannels is discussed here A neutronics approach basedon using control rods burnable absorbers and axial fuelenrichment variance to change the power distribution will bestudied in the future [10]
As shown in Figure 2 moderator enters the channelfrom the moderator upper plenum flows downwards in thechannel and then exits to the lower plenum The pressurebalance through the moderator channel is dominated bythree terms the elevation pressure loss (gain in this case) and
the entranceexit pressure lossesThe pressure balance can bewritten as follows
int
out
in120588119892119889119897 minus
1
2119860
2
mod
119870119898
2
120588
119900
= Δ119875 (1)
where Δ119875 represents the pressure difference of upper andlower plenum for an individual channel In RELAP5 theabrupt orifice friction lost coefficient is defined as [11]
119870 = (
119860mod119860
119888
minus 1)
2
(2)
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 5
Nonreverse channel
1 2 3 40
1
2
3
Pow
er (M
W)
1 2 3 40
1
2
3Po
wer
(MW
)
Reverse channel
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
700
800
900
1000
1100
1200
1300
Fuel
tem
pera
ture
(K)
1 2 3 4
600
650
700
750
800
850
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
1 2 3 4
600
650
700
750
800
850
Coolant moderator Coolant
moderator
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
1 2 3 4100
200
300
400
500
600
Core height (m)
Equi
vale
nt d
ensit
y (k
gm
3)
r = 020
r = 018
r = 015 r = 020
r = 018
r = 015
Figure 4 Power fuel temperature moderator and coolant temperature and equivalent density profiles in three assemblies for three orificecases
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
6 Science and Technology of Nuclear Installations
where 119860119888is the physical minimum flow area It is defined as
119860
119888= 062119860
119900+ 038
119860
4
119900
119860
3
mod (3)
where119860119900is cross-section of orifice and119860mod is cross-section
of moderator channelSince the hot channel has a lower water density than
the normal channel the elevation pressure loss is lower Tobalance (1) the flow rate in the hot channel has to decreaseHowever by reducing the orifice size 119860
119900 the increased loss
coefficient 119870 ((2) and (3)) suggests that a smaller change inmass flow rate is needed and the reversal can be preventedWhile the neutronics may mitigate the effect because of thelower moderation due to lower density in the hot channel acoupled analysis will be helpful to investigate the possibilityof this reversal
In the following section the results from three uniformorifice size cases are displayed followed by the results fromone case with varied orifices corresponding to differentassembly powers
4 Results
41 Uniform Orifice Case The results in Figures 3 and 4 aregenerated at the beginning of cycle for three different uniformorifice sizes indicated by the ratio of their area to themoderator channel area 119903 The fuel arrangement is shown inFigure 1There are no control rods or burnable absorbers usedin this problem
Figure 3 shows moderator flow rate equivalent densityand total assembly power in each assembly of the quartercore The equivalent density is defined as
120588eq =sum
12
119894=1
(120588cool119894119881cool119894 + 120588mod119894119881mod119894)
sum
12
119894=1
(119881cool119894 + 119881mod119894) (4)
where the summation is over the 12 axial nodes 119894 The resultsfor 119903 = 020 are repeated here for comparison purposesand show the reversed flow in the moderator channels oftwo assemblies As the area ratio is reduced to 119903 = 018the flow reversal is avoided and downward flow occurs inall assemblies The assembly power for those assembliesincreases because the average equivalent density increasesimproving the overall moderation With further reduction inthe orifice area to 119903 = 015 even more of the moderator flowis distributed to the assemblies that previously showed reversemoderator flow Although the equivalent density is still muchlower than the other assemblies these assemblies are now thehighest power assemblies in the core
Figure 4 shows the axial variations in the assembly powercoolant and moderator temperatures and equivalent densityfor an assembly that experiences flow reversal (2D) and foran assembly that does not (2C) In the reference case thepower distribution is shifted towards the bottom of the coresince the flow reversal reduces the moderation in the topof the core Although the nonreversed assemblies do notexperience any local reduction in themoderation (equivalentdensity) their power distribution is shifted down somewhat
Table 3 Orifice arrangement
02 02 02 02 02 02 0202 025 02 025 02 0225 0202 02 02 02 0225 0202 025 02 0225 02 0202 02 0225 02 0202 0225 02 0202 02
The largest local power density in the core is found in thereversed channel even though it is not the highest powerassembly in the reference case By contrast in the cases withflow reversal suppressed 119903 = 018 and 119903 = 015 the axialpower distribution is similar in all assemblies including thehighest power assemblies in which flow reversal occurredwith 119903 = 020 One apparent benefit to the downwardshifted power distribution is a reduction in claddingfueltemperatures since the maximum power occurs at a locationwith lower coolant temperatures However the strong axialvariation in power for the reversed channel could presentother problems In particular as a result of nonuniformburnup the flow reversal may vanish over the cycle as theaxial power distribution in these channels responds
Based on the results of Figures 3 and 4 it is possible toprevent the reversal by using uniform orifice area ratio 119903 lt018 though from consideration of safety margin a lowervalue is preferred
42 Nonuniform Orifice Case In traditional PWR designorifices are used to manage the distribution of coolant flowbased on the power distribution Following this example thisstudy developed an orifice pattern inwhich larger orifice sizesare applied to hot channels to deliver more flow and lowermoderator temperatures to prevent reversal This approachleads to larger orifice flow area ratios and lower overall pres-sure dropsThe following results show comparison between avaried orifice case and a uniform orifice case without reversal(119903 = 015)
The variation of area ratio 119903 is chosen based on theexpectation of higher assembly power for the most reactive(fresh) assemblies Table 3 shows the 119903 value of each assemblyThe results of the varied 119903 case are similar to those of 119903 = 015case although they show a slightly higher degree of powerpeaking among assemblies Figure 5 shows the moderatorflow rate equivalent density and assembly power across thequarter core of the two cases and Figure 6 compares thepower and temperature profiles in corresponding channelsThese results demonstrate that varied orifice sizes can preventreversal with a larger orifice size that is required for theuniform orifice size solution
5 Discussion
In the current US reference design changing the orifice sizecan prevent flow reversal and manage axial power peaking atsteady state condition However the assembly power peaking
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 7
0
2 4 6
1234567
061
081
102
2 6
1234567
0 0
200
400
600
2 4 46
1234567
Moderator flow rate (kgs) Normalized assembly power
2 4 6
1234567
0
061
081
102
2 4 6
1234567
0
200
400
600
2 4 6
1234567
Moderator flow rate (kgs) Normalized assembly power
minus149 minus127 minus144 minus127 minus150 minus148 minus161
minus127 minus109 minus119 minus108 minus126 minus151 minus162
minus144minus119 minus139 minus116 minus126 minus157
minus127 minus108 minus116 minus113 minus148 minus162
minus150 minus126 minus126 minus148minus161
minus148 minus151 minus157 minus162
minus161 minus162 minus15
minus10
minus5
0
minus15
minus10
minus5
minus142 minus128 minus139 minus129 minus142 minus142 minus151
minus128 minus102 minus124 minus101 minus128 minus131 minus151
minus139 minus124 minus135 minus123 minus117 minus148
minus129 minus101 minus123 minus112 minus142 minus151
minus142 minus128 minus117 minus142 minus151
minus142 minus131 minus148 minus151
minus151 minus151
Equivalent density (kgm3)
Equivalent density (kgm3)
539 488 528 489 541 537 596
488 418 472 414 486 502 607
528 472 515 467 457 567
489 414 467 438 538 604
541 486 457 538 597
537 502 567 604
596 607
103 114 106 114 101 102 071
114 124 116 122 114 115 063
106 116 109 116 121 091
114 122 116 121 102 066
101 114 121 102 071
102 115091066
071063
Varied r
r = 015
534 485 523 486 537 533 593
485 408 471 406 485 492 604
523 472 510 469 449 563
487 406 469 434 534 601
537 485 449 534 594
533 492 563 601
593 604
103 115 106 114 101 102 071
115 122 117 121 115 113 063
106 117 110 118 120 091
114 121 118 121 103 066
101 115 120 103 072
102 113 091 066
071 063
Figure 5 Moderator flow rate equivalent density and normalized assembly power (reference value 2459MW) in varied 119903 case and 119903 = 015case
0
1
2
3
Pow
er (M
W)
800
1000
1200
Fuel
tem
pera
ture
(K)
1 2 3 4
600
700
800
Core height (m)1 2 3 4
Core height (m)1 2 3 4
Core height (m)
Mod
erat
or an
d co
olan
t te
mpe
ratu
re (K
)
Varied r r = 015
Varied r r = 015
Varied r r = 015
Figure 6 Power fuel temperature and moderator and coolant temperature in hot channel in varied 119903 case and 119903 = 015 case
is large and may lead to detrimental hot spot effects Andfurthermore the reversal during depletion can be moderatedby using control rods burnable absorbers and varying thefuel enrichment in the further analysis
Noticing that the density change across the supercrit-ical point has a tendency to reverse the moderator flowas in Okarsquos original design the water rods are insulatedfrom the hot coolant of the fuel which is surroundedby almost stagnant water which has an insulation coveraround to provide adequate moderation the same kindof reversal should be avoided in such design Howeverthese insulated water rods are replaced with the similarwater rods with US reference SCWR in his later designs[1 10] While in mixed spectrum reactor design whichseparates the higher densityhigher moderation water and
lower densitymoderation water to thermal and fast zonesthis kind of reversal can be mitigated though the reversaldue to other effects still appeared during the accidents[5 12]
6 Conclusion
A coupled code package PARCS and RELAP5 is introducedto study the SCWR reactor core Flow reversal in downwardflowingmoderator channels is foundusing the coupled codesThe reason of the reversal is the buoyancy and densitychange across the supercritical pointUsing both uniformandnonuniform orifices in moderator channels to prevent thereversal is studied Results showed that with uniformorifices
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
8 Science and Technology of Nuclear Installations
orifice-moderator area ratio less than 018 is needed withnonuniformorifice higher area ratio can prevent the reversal
Nomenclature
119860 Area (m2)119870 Friction loss coefficient119881 Volume (m3)119892 Acceleration of gravity (ms2)120588 Density (kgm3)120588eq Equivalent density (kgm3)119900 Orificemod Moderator119888 Vena-contract
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the sponsors Nuclearand Radiation Safety Center of Ministry of EnvironmentProtection of China with Project no ZD1301-WXHT-01-1 and Ministry of Education of China with Project no20100073120049
References
[1] Y Oka and S Koshizuka ldquoSupercritical-pressure once-throughcycle light water cooled reactor conceptrdquo Journal of NuclearScience and Technology vol 38 no 12 pp 1081ndash1089 2001
[2] J Yoo Y Ishiwatari Y Oka and J Liu ldquoComposite core designof high power density supercritical water cooled fast reactorrdquoin Proceedings of the Global International Conference TsukabaJapan 2005 Paper 246
[3] J Buongiorno ldquoProgress report for the FY-03 Generation-IVRampD activities for the development of the SCWR in USrdquo TechRep INEELEXT-03-01210 2003
[4] T K Kim P P H Wilson P Hu and R Jain ldquoFeasibility andconfiguration of a mixed spectrum supercritical water reactorrdquoin Proceedings of the Physics of Fuel Cycles andAdvancedNuclearSystemsmdashGlobal Developments (PHYSOR rsquo04) pp 1513ndash1523Chicago Ill USA April 2004
[5] Z H Xu D Hou S W Fu Y Yang and X Cheng ldquoLoss of flowaccident and its mitigation measures for nuclear systems withSCWR-Mrdquo Annals of Nuclear Energy vol 38 no 12 pp 2634ndash2644 2011
[6] P MacDonald ldquoFeasibility study of supercritical light watercooled reactors for electric power productionrdquo Idaho NationalEngineering and Environmental Laboratory Report INEELET-04-02530 2005
[7] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator User ManualDraft (111004) 2004
[8] HELIOS manual Scandpower 1997[9] P P H Wilson and P Hu ldquoReactor analysis for counter-
flowing moderator and coolant in a supercritical water reactorrdquo
in Proceedings of the 14th International Conference on NuclearEngineering (ICONE rsquo06) Miami Fla USA July 2006
[10] K Kamei A Yamaji Y Ishiwatari Y Oka and J Liu ldquoFuel andcore design of super light water reactor with low leakage fuelloading patternrdquo Journal of Nuclear Science and Technology vol43 no 2 pp 129ndash139 2006
[11] RELAP5 manual vol 1 pp 193 July 2003[12] D H Zhu W X Tian H Zhao Y L Su S Z Qiu and
G H Su ldquoComparative study of transient thermal-hydrauliccharacteristics of SCWRs with different core designrdquo Annals ofNuclear Energy vol 51 pp 135ndash145 2013
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Research ArticleCode Development in Coupled PARCSRELAP5 forSupercritical Water Reactor
Po Hu1 and Paul Wilson2
1 School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China2Department of Engineering Physics University of Wisconsin-Madison Madison WI 53705 USA
Correspondence should be addressed to Po Hu pohusjtueducn
Received 6 January 2014 Revised 9 April 2014 Accepted 10 April 2014 Published 8 May 2014
Academic Editor Jiejin Cai
Copyright copy 2014 P Hu and P WilsonThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The new capability is added to the existing coupled code package PARCSRELAP5 in order to analyze SCWR design undersupercritical pressure with the separated water coolant and moderator channels This expansion is carried out on both codes InPARCS modification is focused on extending the water property tables to supercritical pressure modifying the variable mappinginput file and related code module for processing thermal-hydraulic information from separated coolantmoderator channels andmodifying neutronics feedbackmodule to deal with the separated coolantmoderator channels In RELAP5modification is focusedon incorporatingmore accuratewater properties near SCWRoperationtransient pressure and temperature in the code Confirmingtests of the modifications is presented and the major analyzing results from the extended codes package are summarized
1 Introduction
The supercritical water reactor (SCWR) is a generation IVnuclear reactor concept characterized by its system simplifi-cation and high thermal efficiency Due to its higher oper-ating pressure and temperature separated moderator andcoolant channels and a strong coupling between power (neu-tronics calculation) and moderator temperature (thermal-hydraulic (TH) calculation) because of a large densityvariation of water (100 to 700 kgm3) existing LWR codes arenot capable of analyzing SCWR design without appropriatemodifications [1] Yamaji et al have shown coupled neu-tronics and TH analysis of high temperature supercritical-pressure light water reactor (SCLWR-H) The code packageincludes SRAC code system (neutronics) from Japan AtomicEnergy Research Institute (JAERI) and SPROD code (TH)from University of Tokyo Buongiorno and Macdonald pre-sented and analyzed the US reference SCWR design usingRELAP5 with a point kinetics model [2 3]The current studydeveloped a neutronics and TH coupled analysis capabilityfor the US reference design by extending existing LWRanalysis code package that is the core simulator PARCS andtheTHcodeRELAP5which have been verified for analyzingPWR and BWR in coupled mode and are easily accessible
for academic purposes [4] this paper discusses the codesmodifications and presents the preliminary tests confirmingthe major extensions in code coupling module and nuclearcross section feedback module in PARCS and water propertymodule in RELAP5 The SCWR analyzing results using theextended code package are summarized here and the detailsare discussed in another paper [5]
2 Existing Coupling Mechanism
Current study analyzes the SCWR using extended codepackage PARCSRELAP5
PARCS [6] is a 3D reactor core simulator developed inPurdue University It solves the steady state time-dependentandmultigroupneutron diffusion equation and SP3 transportequation to predict the dynamic response of the reactor toreactivity perturbations PARCS is applicable to both PWRand BWR and can be coupled directly to the TH system codeRELAP5
RELAP5 [7] is a TH code designed for best-estimatetransient simulation of light water reactor system It wasdeveloped at the Idaho National Lab for the US NuclearRegulatory Commission It is capable of modeling coupled
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 286434 8 pageshttpdxdoiorg1011552014286434
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
2 Science and Technology of Nuclear Installations
Other modules
RDMR
Other modules
PDMR
GI
RELAP5 PARCS
Variable mapping file
Figure 1 PARCSRELAP5 coupling mechanism
behavior of the reactor coolant system and core for accidentsand transients using eight field equationsThe version used incurrent study is RELAP5MOD33
In order to simulate the feedback between the thermal-hydraulics and the neutronics the field equations of RELAP5can be coupled to either a built-in point kinetics model or a3D neutronics code PARCS By using the 3D kinetics codewe can calculate power distribution in a new type of reactordesign such as SCWR instead of appealing to typical LWRparameters like in point kinetics model
To couple PARCSRELAP5 in the point of view ofPARCS is to replace the internal thermal hydraulics solverin PARCS with an external TH code which is RELAP5in this case (Figure 1) As the solving scheme of a steadystate problem shown in Figure 2 PARCSperforms neutronicscalculation to generate new power profile with nuclear crosssection information based on the temperature data fromRELAP5 then RELAP5 receives the updated power profilefrom PARCS and performs TH calculations to generate thenew temperatures of fuel moderator and coolant and passesthe temperature information back to PARCS The coupledsimulation will be ended when the iteration in PARCSconverges
The RELAP5 data map routine (RDMR) module inRELAP5 is designed to communicate with neutronics codePARCS through a general interface (GI) module in PARCSThe PARCS-specific data map routine (PDMR) module inPARCS is the counterpart to RDMR in RELAP5 and itfunctions as an interface between PARCS and external THcodes such as RELAP5 and TRAC-M through the GImodule PDMR is designed to maintain consistency with therequirements of both the GI and the RDMR while preparingdata to be transferred to RELAP5 A space-dependent vari-able mapping input file read by PDMR module defines thecorresponding nodes between PARCS and RELAP5 modelsThe parallel virtualmachine (PVM) code is utilized to controlthe communications between two codes
The US reference design is essentially a light waterreactor (LWR) operating at higher pressure and temperaturewith a direct cycle Comparing to a normal PWR the majordifference is that SCWR uses light water as moderator and
Start
Coarse mesh finite difference (CMFD) solver
Nodal expansion Method analytic Nodal method
(NEMANM) solver
Updated power profile
(Internalexternal)thermal
hydraulics solver
converge
End
Updatetemperature
profile
Updatenuclear cross
section
No
Yes
TH
Dat
aN
eutro
nics
Keff Ψ and Tfueltr
ansfe
r
Figure 2 Solving scheme for steady state eigenvalue problem inPARCS
coolant in separated channels as shown in Figure 3 the feedwater temperature is 280∘C and outlet temperature is 500∘Cat pressure of 25MPa [2 3]
3 Modifications on PARCS
Because the SCWR reference design has higher operatingpressure and temperature and utilizes the new claddingmaterial and separated coolant and moderator channels [8]in order to analyze it the following modules in PARCS needto be modified
(i) water and cladding thermophysical property func-tions or tables are modified accordingly
(ii) variable mapping input file and PDMR module needto be modified to deal with information from extraflow channel in order tomodel separated coolant andmoderator flow channels
(iii) the nuclear macroscopic cross section updatingmod-ule in PARCS should be extended to include thefeedback based on not only fuel and coolant but alsomoderator thermophysical properties the accessorymodification in PARCS also includes the new inputlines for SCWR specially in the input files and the newvariable storage file for SCWRproblem in source files
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 3
Control rod (times16)
Instrumentation pin
Fuel rod (times300) Water rod (times36)
Figure 3 The cross sections assembly of US reference design [2]
31 Modification of Thermophysical Properties of Water andCladding In coupled simulation mode (PARCSRELAP5)the thermophysical properties will be supplied by TH solverRELAP5 however in the initialization process in PARCSthe functions describing thermophysical properties of waterand cladding material functions are still called Thereforethe modifications in these functions are needed for SCWRanalysis
The thermophysical properties of water are originallydescribed by simple polynomial equations as a function oftemperature or enthalpy under PWR or BWR operating pres-sure Therefore a water density function under supercriticalpressure is added Because of the dramatically changingwaterdensity near the pseudocritical point a more sophisticatedscheme specifying water density under 25MPa based onNBSNRC steam tables [9] is adopted using lookup tables anddata are arranged in uniform intervals of temperature (01 K)or enthalpy (1 KJKg) and can be searched by direct index
Because MA956 is used as cladding material in SCWRreference design instead of zircalloy for ordinary PWRsor BWRs in original PARCS the polynomial functions ofthe conductivity and thermal capacity of MA956 based ontabulated data are implemented in the code for SCWR design[10]
32 Modification in Nuclear Cross Section Feedback ModuleSCWR reference design has separated coolant andmoderatorchannels so water flowing in the separated channels hasdifferent temperatures and densities Therefore the neutron-ics cross section feedback mechanism in PARCS should beable to handle the moderator and coolant themophysicalproperties separately
The original PARCS can update the macroscopic crosssection based on fuel temperature coolant temperaturecontrol rod positions and burnable poison concentrationand the modified PARCS can also update the cross sectionbased onmoderator density and temperature As shown in (1)underlined parameters are newly added term (120597Σ120597119879
119898)Δ119879
119898
represents the cross section feedback due to the mod-erator temperature change and term (120597Σ120597119863
119898)Δ119863
119898+
(120597
2
Σ120597119863
2
119898
)(Δ119863
119898)
2 represents cross section feedback due tothe moderator density change notice that the dependence ofmoderator temperature is modeled as linear and dependenceof moderator density is quadratic There are two partsinvolved in the modification firstly a new option is addedinto cross section feedback module in PARCS secondly thecross section data file is updated to store the cross sectioninformation from different combinations of moderator andcoolant themophysical properties fuel temperature and con-trol rod position the data file is generated using GenPMAXScode based on calculation results from lattice code HELIOS[11]
Σ (120572 119879
119891 119879
119898 119879
119888 119863
119898 119863
119888) =Σ
119903+ 120572ΔΣ
119888119903+
120597Σ
120597radic119879
119891
Δradic119879
119891
+
120597Σ
120597119879
119898
Δ119879
119898+
120597Σ
120597119879
119888
Δ119879
119888
+
120597Σ
120597119863
119898
Δ119863
119898+
120597
2
Σ
120597119863
2
119898
(Δ119863
119898)
2
+
120597Σ
120597119863
119888
Δ119863
119888+
120597
2
Σ
120597119863
2
119888
(Δ119863
119888)
2
(1)
33 Modifications in Variable Mapping File and CouplingModule PARCS is coupled to RELAP5 using PDMRmodulebased onmapping rules defined in the space-dependent vari-able mapping input file Because the SCWR reference designhas separated moderator and coolant channels extendedmapping rules should be supplied in the variable mappinginput file and corresponding modifications are needed inboth PARCS and RELAP5
As shown in Table 1 an original mapping input filecontains four cards ldquoTriprdquo ldquoDOPLrdquo ldquoTable 1rdquo and ldquoTable 2rdquoThe ldquoTable 1rdquo card defines the mapping rule between hydro-dynamic volumes in RELAP5 model and neutronics nodesin PARCS model ldquoTable 2rdquo card defines the mapping rulebetween heat structures in RELAP5 model and neutronicsnodes in PARCS model These two cards have multiple inputlines in the same format
In some cases the number of neutronics nodes in PARCSand the number of hydrodynamic volumesstructures inRELAP5 used to represent same physical region are differentThe weighting factors are used to lump adjacent nodes orvolumesstructures to make the mapping possible
These mapping tables are sufficient for ordinaryPWRBWR designs but not for the current SCWR designThe separation of moderator and coolant in SCWR instead of
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
4 Science and Technology of Nuclear Installations
Table 1 PARCSRELAP5 mapping input file
lowast
Table 1lowastRELAP volume number PARCS node
numberWeightingfactor
335010000 1 1335020000 2 1335030000 3 1
335880000 88 1335890000 89 1335900000 90 1lowast
lowastHeat structure to node tablelowast
Table 2lowastRELAP structure number PARCS node
numberWeightingfactor
3360001 1 13360002 2 13360003 3 1
3360088 88 13360089 89 13360090 90 1
lowastData ignored from the original table And the ldquo rdquo means the more similar
input lines are ignored
the combined moderatorcoolant flow in PWRBWR meansfor each neutronics node in SCWR PARCS model there willbe two corresponding hydrodynamic volumes in RELAP5one representing coolant flow and the other moderator flowUsing the tables described above only one hydrodynamicvolume can be matched to each neutronics node
Therefore both the variable mapping file and relatedsubroutines in PDMR module in PARCS are extended tosolve this problem In the new mapping input file a fifthcard ldquoTable 3rdquo is added to map hydrodynamic volumesrepresenting moderator flow to neutronics nodes The orig-inal ldquoTable 1rdquo card now only manages the mapping betweenhydrodynamic volumes representing coolant flow and neu-tronics nodes
Appropriate modifications in PDMA module are intro-duced to receive data from the newly added mapping tableldquoTable 3rdquo and integrate these data to a permutated matrixtogether with the mapping information from ldquoTable 1rdquo andldquoTable 2rdquo then send the matrix to RELAP5 together with thenewly added control options for SCWRsimulation in coupledmode And the error checking subroutine is also updatedfor new mapping table ldquoTable 3rdquo and moderator thermalproperties
150 200 250 300 350 400 450 500 55025
25526
26527
27528
28529
29530
Pres
sure
(MPa
)
New water table Original water table
Density (kgm3)
675K larr 654K
Figure 4 Density versus pressure in isotherm from original andmodified water tables of RELAP5
4 Modification on RELAP5
There are two modifications needed in the current version ofRELAP5MOD33 in the point of view of analyzing SCWRRELAP5 is not stable at pressure above 259MPa where theSCWR transients usually happen because a coarse grid insupercritical point region is used in water property tablethe error checking routine in the module RDMR (RELAPdata mapping routines) in RELAP5 treats the water densitybelow 035 gcm3 as an error but the water density can reach01 gcm3 crossing pseudocritical point in SCWR
41 Modification in Water Property Table In RELAP5 thegrid of the water property table is calculated by inputtemperature and pressure values The original temperaturevalues consist of 157 points with 15 points covering thesupercritical temperature range 645Kndash675K and 14 pointscovering the higher temperature region (700Kndash6000K) andthe pressure values consist of 116 points with 10 pointscovering the pressure range from 209MPa to 300MPa and 5points covering higher pressure region (300MPandash999MPa)
The modified input file increases the number of thepoints in the same ranges for both temperature (645Kndash675K)and pressure (209MPandash300MPa) now in new temperatureset there are 184 points with 37 points covering the rangeand the increment is one degree among most points inthe new pressure set there are 578 points with 468 pointscovering the range To accommodate these densifications thecorresponding variable arrays are expanded accordingly
The improvement from this modification can be illus-trated in Figure 4 in which the pressure-density correlationsin isotherms (119875(119863 119879)) are shown The original water tableuses only two pressure points (25MPa and 30MPa) andthree temperature points (654K 660K 675K) to representthe region in the plot while the new water table uses 301pressure points and 22 using interpolation three straight-line isotherms are used in original water table but 22 curvedisotherms are used in newwater table After themodification
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 5
Table 2 SCWR parameters
Fuel Pin Fuel assemblyFuel material UO2 Number of fuel rods 240Fissile enrichment 5 Number of burnable absorber 60UO2 density 104215 gcm3 Number of water rods 36Fuel radius 0439 cm Number of control rods 12Pellet to cladding gap 0008 cm Water rod width 336 cmCladding thickness 0063 cm Water rod wall thickness 004 cmFuel pitch 112 cm Fuel assembly pitch 2882 cmPD 1098 Assembly wall thickness 03 cmCladding and core structure material MA956 Interassembly gap 02 cm
Burnable absorber CoreBurnable absorber material ZrB2 Thermal power 3575MWZrB2 density 608 gcm3 Number of fuel assemblies 145Fuel material UO2 Heated fuel height 427mFissile enrichment 5 Total fuel pin height 487mUO2 density 104215 gcm3 Effective diameter 393mFuel radius 0439 cm Volumetric power density 69MWm3
BA cover thickness 00044 cm Average linear heat rate 192 kWmPellet to cladding gap 00036 cm Fuel depletion plan 3 cyclesCladding thickness 0063 cm Average burnup 012525GWdMTU
Control rod Thermal-hydraulic parametersControl rod material B4C System pressure 25MPaB4C density 259 gcm3 Coolant flow rate 1843 kgsControl rod radius 0662 cm Bypass ratio 120578 10 (184 kgs)Control rod guide tube inner radius 0912 cm RPV inlet temperature 280∘CControl rod guide tube thickness 004 cm RPV outlet temperature 500∘C
Thermal efficiency 4480
Table 3 Temperatures and densities of moderator and coolant
Node number Moderator CoolantTemperature (∘C) Density (kgm3) Temperature (∘C) Density (kgm3)
1 3538 6129 3541 61162 3537 6131 3728 52263 3524 6177 3818 41934 3501 6251 3848 32485 3474 6337 3871 25546 3443 6431 3915 20487 3405 6537 3995 16848 3359 6662 4126 14169 3299 6809 4312 121610 3220 6991 4552 106511 3112 7218 4810 95812 2968 7489 4904 927
RELAP5Mod33 can calculate the water properties underpressure up to 30MPa without large error as in original watertable
42 Modification in Error Checking Routines OriginallyRDMR checks if the water density is between 1050 kgm3 and305 kgm3 and this checking range is expanded to between
1050 kgm3 and 5 kgm3 to accommodate the water densitychange crossing the supercritical point
5 Preliminary Test of the Modifications
The validation of the extended codes cannot be implementedwithout support of the related SCWR experiment which
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
6 Science and Technology of Nuclear Installations
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 1
HELIOSPARCS
1 2 3 4 5 6 7 8 9 10 11 12Node number
Transport cross section of energy group 2
Mac
rosc
opic
cros
s
780E minus 01
760E minus 01
740E minus 01
720E minus 01
700E minus 01
680E minus 01
660E minus 01
640E minus 01
235E minus 01
230E minus 01
225E minus 01
220E minus 01
215E minus 01
210E minus 01
205E minus 01
200E minus 01
sect
ion
(cm
minus1)
Mac
rosc
opic
cros
s se
ctio
n (c
mminus1)
Figure 5 Comparison of cross sections from PARCS and HELIOS
Table 4 Densities from coupled PARCS node and RELAP5 volumes
From Table 3 in mapping file Density (kgm3)Hydraulic volume number Node number Weighting factor RELAP5 PARCS753030000 274 1 65984 6598457753040000 475 1 66053 6605327753050000 676 1 66339 6633935753060000 877 1 66855 6685484753070000 1078 1 67567 6756677753080000 1279 1 68422 6842207753090000 1480 1 69364 6936387753100000 1681 1 70333 7033298753110000 1882 1 71408 7140801753120000 2083 1 72654 7265369753130000 2284 1 73996 7399585753140000 2485 1 75407 7540657
is not available for this concept design The verificationof the extended codes could be done with the help ofother verified SCWR-capable codes which is not accessiblecurrently However some preliminary tests presented herecan help to confirm the new added functions in the modifiedcodes for SCWR analysis working properly
51 Cross Section Feedback Module Current coupled PARCSuses PMAX files to supply nuclear cross section data gen-erated by lattice code HELIOS And the PMAX files areproduced by the GenPMAXS code which is an interfacebetween lattice codes and PARCS and it already has thecapability to generate the cross section data based on sep-arated moderator and coolant channels [11] According tothe assembly geometry shown in Figure 3 and parametersin Table 2 macroscopic cross sections are calculated for the
same assembly with PARCS and HELIOS and the coolantand moderator thermal parameters in this test are shown inTable 3 A comparison of transport cross sections generatedby PARCS using the modified cross section feedback modulefrom PMAX file and transport cross sections produceddirectly by HELIOS in two energy groups are shown inFigure 5 The difference is acceptable considering that theinterpolation of PMAX file data is used in PARCS moduleThe same comparisons are also accomplished successfully forabsorption cross sections fission cross sections and capturecross sections of Xenon and Samarium
52 Code Coupling Module To confirm the coupledPARCSRELAP5 is transporting the mapped moderatorinformation correctly a simple coupled SCWR calculation iscarried out A part of Table 3 of mapping file which displays
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 7
Mod
erat
or ch
anne
l
Wat
er ro
d
Coo
lant
chan
nel
Fuel
rod
Figure 6 Flow path model of RELAP5 test
the corresponding hydrodynamics volume and nodes intwo codes and the coupling weighting factor is shown inTable 4 The comparison of the moderator densities fromPARCS and RELAP5 is also shown in Table 4 It shows thecoupled hydrodynamic volumes in RELAP5 and nodes inPARCS are sharing the samemoderator densitiesThe similarcomparisons are also passed for moderator temperaturecoolant temperature and density fuel temperature andpower
53 RELAP5 Modification for Dealing with SupercriticalPressure The original RELAP5 failed in the middle of thecalculation because of the escalation of the fluctuation both inpressure and temperature at supercritical pressure while themodified RELAP5 calculated successfully with no fluctuationnoticed In order to demonstrate the capability of the modi-fiedRELAP5 a simplified testmodel inwhich two connectingpipes representing moderator channel and coolant channelwith counter flowing heatedwater passing through are shownin Figure 6 and the moderator inlet pressure is increasedlinearly from 26MPa to 271MPa and coolant outlet pressurefrom 255MPa to 266MPa within 3000 seconds The resultsare shown in Figure 7
6 Discussion
The modifications in coupled codes PARCSRELAP5 havebeen discussed and verified the newly developed codesgained the capability simulating the separatedmoderator andcoolant flow channel simulating supercritical water beyondsupercritical point and getting neutronics feedback fromseparatedmoderatorThe coupled codes have been applied toanalyze SCWR [12] amoderator flow reversal has been foundduring burnup and transient cases and because the separatedhighest power channel and highest cladding surface temper-ature channel the maximum cladding temperature is lowerthan previous cases
For other transients such as LOCA in which largepressure excursion exists the current modification is not
210
220
230
240
250
260
270
117
735
352
970
588
110
5712
3314
0915
8517
6119
3721
1322
8924
6526
4128
1729
9331
6933
4535
2136
9738
7340
4942
2544
0145
7747
5349
2951
0552
8154
57
Data point number
Pres
sure
(Pa)
Original RELAP5Modified RELAP5
645
650
655
660
665
670
675
121
843
565
286
910
8613
0315
2017
3719
5421
7123
8826
0528
2230
3932
5634
7336
9039
0741
2443
4145
5847
7549
9252
0954
26
Tem
pera
ture
(K)
Data point number
Original RELAP5Modified RELAP5
times105
Figure 7 Pressure and temperature from test case with original andmodified RELAP5
enough to study the related system behavior It is becausethe large depressurization in those transients introduces thecomplicated heat transfer and flow dynamics phenomenacrossing pseudocritical point sometimes a two-phase flowfurther investigation to establish appropriate model based onrealistic experiment data is needed such as how to define thevoid fraction while crossing the pseudocritical point
Nomenclature
119881 Volume (m3)119863 Density (kgm3)119879 Temperature (∘C)Σ Macroscopic cross section (mminus1)120578 Bypass ratio120572 control rod insertion119872 Moderator119888 Coolant119891 Fuel
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
8 Science and Technology of Nuclear Installations
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The authors would like to thank the flowing sponsors Grantsno DE-FG03-01SF22328 and 2401-UW-DOE-4423 from theDepartment of Energy of US Project 11205098 supported byNational Natural Science Foundation of China and Project20100073120049 supported by Ministry of Education ofChina
References
[1] J Starflinger N Aksan D Bittermann et al ldquoRoadmap forsupercritical-water-cooled reactor RampD in Europerdquo in Proceed-ings of the Atoms for Prosperity Updating Eisenhowerrsquos GlobalVision for Nuclear Energy (GLOBAL rsquo03) pp 1137ndash1142 NewOrleans La USA November 2003
[2] J Buongiorno and P E Macdonald ldquoProgress report for theFY-03 generation-IV RampD activities for the development ofthe SCWR in the USrdquo Tech Rep INEELEXT-03-01210 IdahoNational Engineering and Environmental Laboratory 2003
[3] C B Cliff J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-trip eventsrdquo in Proceedings of the International Conferenceon Advanced Nuclear Power Plants and Global Environment(ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[4] A Bousbia-Slah J Vedovi F DrsquoAuria and K Ivanov ldquoAnalysisof the peach bottom 2 turbine trip 2 experiment by coupledRELAP5-PARCS there-dimensional codesrdquoNuclear Science andEngineering vol 148 no 2 pp 337ndash353 2004
[5] P O Hu and P P H Wilson ldquoSupercritical water reactorsteady-state burnup and transient analyses with extendedPARCSRELAP5rdquo Nuclear Technology vol 172 no 2 pp 143ndash156 2010
[6] T Downar D Lee Y Xu T Kozlowski and J StaudenmierPARCS v26 US NRC Core Neutronics Simulator USER MAN-UAL Draft (111004) Purdue University and NRC 2004
[7] Nuclear Safety DivisionRELAP5MOD33 CodeManual Infor-mation System Laboratories 2004
[8] C B Davis J Buongiorno and P E Macdonald ldquoA paramet-ric study of the thermal-hydraulic response of supercriticallight water reactors during loss-of-feedwater and turbine-tripeventsrdquo in Proceedings of the International Conference onAdvanced Nuclear Power Plants and Global Environment (ANPGENES4 rsquo03) Kyoto Japan 2003 paper no 1009
[9] L Haar J S Gallagher and G S Kell NBSNRC Steam TablesHemisphere Publishing Corporation McGraw-Hill New YorkNY USA 1984
[10] httpwwwspecialmetalscomdocumentsIncoloy20alloy20MA956pdf
[11] Y Xu and T Downar GenPAMXS Manual Purdue University2005
[12] P Hu and P Wilson ldquoSupercritical water reactor steady stateburnup and transient analysis with extended PARCSRELAP5rdquoin Proceedings of the 4th International Symposium on Supercrit-ical Water-Cooled Reactors Heidelberg Germany 2009 paperno 13
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Research ArticlePreliminary Development of Thermal Power Calculation CodeH-Power for a Supercritical Water Reactor
Fan Zhang Dao-gang Lu Dan-ting Sui Bo Yuan and Chao Guo
School of Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Fan Zhang hdhxyzf126com
Received 6 December 2013 Revised 18 February 2014 Accepted 18 February 2014 Published 26 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Fan Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
SCWR (Supercritical Water Reactor) is one of the promising Generation IV nuclear systems which has higher thermal powerefficiency than current pressurized water reactor It is necessary to perform the thermal equilibrium and thermal power calculationfor the conceptual design and furthermonitoring and calibration of the SCWROne visual software namedH-Power was developedto calculate thermal power and its uncertainty of SCWR in which the advanced IAPWS-IF97 industrial formulation was used tocalculate the thermodynamic properties of water and steam The ISO-5167-4 2003 standard was incorporated in the code as thebasis of orifice plate to compute the flow rate New heat balance model and uncertainty estimate have also been included in thecode In order to validate H-Power an assessment was carried out by using data published by US and Qinshan Phase II The resultsshowed that H-Power was able to estimate the thermal power of SCWR
1 Introduction
SCWR (Supercritical Water Reactor) is one of the promisingGeneration IV nuclear systems which has higher thermalpower efficiency than current pressurized water reactorCompared to the currently running water coolant reactorsSCWR has the higher thermal efficiency and safety whichmakes it a more promising advanced nuclear energy sys-tem The concept of SCWR was originally put forward byWestinghouse and GE (General Electric) in the 1950s andpreliminarily studied by the United States and the formerSoviet Union from 1950s to 1960s In the 1990s Dobashi et al[1] proposed the concept of SCWR again and made a furtherdevelopment in this area
For reactor operating more safely stably and econom-ically the accurate calibration for real thermal power hasimportant significance in reactor design and analysis It isnecessary to develop a special thermal power calculation codefor SCWR while there is no available program published inthe worldThis paper preliminarily developed visual softwarenamed H-Power to calculate SCWR thermal power and itsuncertainty based on heat balance method which has beenapplied to current PWRs [2]
According to the various conceptual SCWR designs[3ndash5] H-Power divided SCWR into two groups one is thesingle-loop type and the other is the double-loop type Thevalidation of H-Power consists of two parts for the single-loop SCWR the data published by Jacopo [6] was used whilefor the double-loop SCWR the values of Qinshan Phase II[7] were used though it is not the SCWR we just use it forpreliminary validation since the exact detail design data wasrarely published
IAPWS is an international nonprofit association con-cerned with the properties of water and steam particularlythermodynamic properties In 1997 IAPWS adopted theldquoIAPWS Industrial Formulation 1997 for theThermodynamicProperties of Water and Steamrdquo for industrial use [8] calledIAPWS-IF97 for short which replaced the previous industrialformulation IFC-67 [9] published in 1967
We have done lots of researches and work in comparingIAPWS-IF97 with IFC-67 in several aspects The resultshowed that IAPWS-IF97 improves significantly in boundaryconsistency and accuracy and calculation speed [10] whichmakes it more extensive use in power industry nowadays
H-Power adopted IAPWS-IF97 to calculate thermody-namic properties (including specific volume specific
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 279092 10 pageshttpdxdoiorg1011552014279092
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
2 Science and Technology of Nuclear Installations
READDT
THPROP
OUTPUT
ERCALC
NUSOLV
FLOWRT
READDT
OUTPUT
NUSOLV
H-Power
2 loops
1 loop
Figure 1 H-Power modules diagram
enthalpy and viscosity) of water The code covers allrange of IAPWS-IF97 (27315K le 119879 le 107315K 119901 le
100MPa 107315K le 119879 le 227315K 119901 le 50MPa) whichhas been divided into five regions
2 Theoretical Modeling
The modules of H-Power are given in Figure 1 whereREADDT is the reading data subroutine NUSOLV isnumerical calculation subroutine THPROP is the subroutinewhich calculates the thermodynamic properties of water andsteam FLOWRT is the subroutine for flow rate calculationERCALC subroutine is for the uncertainty estimation andOUTPUT is the output data subroutine
H-Power provides a visual interface for users and has highmodule independence which makes it a practical code inSCWR analysis
21 Thermodynamic Properties Subroutine
211 Subroutine Flow Chart The range of IAPWS-IF97 isdivided into five subareas each of them has a basic equationTo make the program more concise and readable thissubroutine used the compiling method of modularizationthat is separate districts of thermodynamics equation werewritten into separate subroutine
We can directly obtain the thermophysical propertiesfrom pressure and temperature values using the basic equa-tions except region 3 Subregion 3 does not have the for-mula which can calculate other various thermal parametersdirectly through the temperature and pressure it can only relyon iteration calculation In this subroutine the first pressurecalculation uses temperature and a small specific volume
which was chosen as initial value If the difference betweenthe calculated value of pressure and user input values ispositive the value of specific volume increases incrementalquantity ratio by half and continues the iteration until thepressure difference is less than condition of convergenceTheiteration is over and other properties can be calculated
Through this kind of iteration and close proximity to theinput value by increasing incremental quantity in halvingbisectionmethod not only the disadvantages of the increasedspecific volume increment are too small to calculate quicklywas avoided but also the accuracy of calculation can beensured
The subroutine of water and steam thermodynamic prop-erties has been totally developed according to the flow chartshown in Figure 2
212 Subroutine Calculation Verification In order to do theverification we list the calculation results together with thosegiven by IAPWS-IF97 in Table 1 We can see that the presentresults are in good agreement with those given by IAPWS-IF97 so that the thermodynamic properties calculated by H-Power are valid
22 Flow Rate Calculation Subroutine The main feedwaterflow rate of the steam generator can be measured by orificeplate which is widely used in measurement of fluid flowThispart is based on the ISO 5167 standard in [11]
As the schematic diagram shown in Figure 3 upstreamfluid pressure 119875
1is obtained by (1) taking pressure loss Δ120596
caused by the existence of orifice plate into account
119875
1= 119875me + 119875119886 + Δ120596 (1)
Δ120596 = Δ119875 times (1 minus 120573
19
) (2)
H-Power adopted the following equation for flow ratemeasurement
119902
119898=
119862
radic1 minus 120573
4
120576 sdot
120587119889
2
4
radic2Δ119875120588
119906 (3)
where 119902
119898is mass flow rate 120573 is ratio of 119889 (diameter of
orifice at operating conditions) and 119863 (diameter of internalpipe at operating conditions) 120576 is expansibility factor (forcompressible fluid 120576 = 1) Δ119875 is differential pressure 120588
119906
is the density of upstream and 119862 is discharge coefficientdetermined by Reader-HarrisGallagher equation as follows
119862 = 05961 + 00261120573
2
minus 0216120573
8
+ 0000521(
10
6
120573
Re119863
)
07
+ (00188 + 00063119860) 120573
35
(
10
6
Re119863
)
03
+ (0043 + 0080119890
minus101198711minus 0123119890
minus71198711) (1 minus 011119860)
120573
4
1 minus 120573
4
minus 0031 (119872
1015840
2
minus 08119872
1015840
2
11
) 120573
13
+ sdot sdot sdot
(4)
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 3
Table1Com
paris
onof
calculationresults
betweenH-Pow
erroutinea
ndIAPW
S-IF97
Region
Parameters
Given
byV(m
3kgminus1
)ℎ(kJkgminus1
)119904(kJkgminus1
Kminus1
)119906(kJkgminus1
)
Subregion1
119879=300K
IF97
000100215168
11533
1273
0392294792
11232
4818
119875=3MPa
H-Pow
er00010021516
11533
127302
03922947924
11232481798
119879=300K
IF97
971180894119890minus4
184142828
0368563852
10644
8356
119875=80MPa
H-Pow
er97118089119890minus4
18414282773
03685638523
10644
835621
Subregion2
119879=300K
IF97
394913866
25499114
5852238967
241169160
119875=00035MPa
H-Pow
er39491386637
25499114
508
852238966
7324116915976
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
Subregion3
119879=66315K
119875=24MPa
IF97
0005613
250075
50320
23660
H-Pow
er00056134399
25007519610
50320333072
23660291590
119879=72315K
119875=50MPa
IF97
0002487
228444
45892
21601
H-Pow
er00024874366
22844399286
458922040321
21600680674
Subregion5
119879=1500K
IF97
13845509
521976
855
965408875
452749310
119875=05MPa
H-Pow
er13
845508987
521976
85512
96540887533
45274931018
119879=2000K
IF97
00311385219
657122604
85364
0523
563707038
119875=30MPa
H-Pow
er00311385218
65712260386
85364
052311
56370703825
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
4 Science and Technology of Nuclear Installations
Input p T
27315 le T le 227315
0 le p le 100
Error and quit
Error and quit
R 5
R 1 R 2 R 2
T T
T
T
T
T
T
T
T
T
P le 10 T ge 107315
F
F
FF
F
F
F
F
F
T le 647096
ps(T)
ps(T)
p = ps
T le 62315 T ge 86315
p23(T)
p lt p23
p lt p23
= 00013
= +
Output result
End
p gt ps
R 4
R 3 iterativecomputations
Figure 2 Flow chart of thermodynamic properties subroutine based on IAPWS-IF97
If119863 lt 7112mm (4) should add the following term
0011 (075 minus 120573) (28 minus
119863
254
) (5)
As we can see from the above equation discharge coef-ficient 119862 depends on the Reynolds number Re
119863 which is
dependent on 119902119898in turn so the calculation of mass flow rate
119902
119898has to be iteratedDiameters in the formula for calculating should be cor-
rected due to the difference of temperature between workingcondition and measurement If there is drain hole (diameter
is 119889119896) on the plate the 119889 should be corrected by the following
equation
119889 = 119889
1198981 + 055(
119889
119896
119889
119898
)
2
(6)
where the 119889119898have already been corrected by temperature as
follows
119889
119898= 119889
0+ 119889
0120582 (119905 minus 119905
0) (7)
where 119889
0is the measurement value under the standard
temperature 1199050 120582 is the coefficient of linear expansion and
119905 is the operating temperature
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 5
Pressure measuring point
Steam generator
Orificeplate
+ Δ120596
Δ120596
Pme + Pa
Pme + Pa
Figure 3 Pressure measuring schematic by orifice plate
Re119863is the Reynolds number calculated by119863 (diameter of
internal pipe at operating conditions) dimensionless param-eters presenting the ratio of the inertia force and viscous forceof upstream calculated by the following equation
Re119863=
4119902
119898
120583120587119863
(8)
where 120583 is viscosity of the fluid at the working conditionswhich is obtained by the thermodynamic properties subrou-tine
119871
1(= 119897
1119863) is the ratio of the distance from the upstream
tapping to the upstream face of the orifice plate and the pipediameter and the value selection of its conditions is asfollows
119871
1=
0 corner tappings
1 119863 and 119863
2
tappings254
119863
flange tappings
119860 = (
19000120573
Re119863
)
08
119872
1015840
2=
2119871
1015840
2
1 minus 120573
(9)
119871
1015840
2
(= 119897
1015840
2
119863) is the ratio of the distance from the down-stream tapping to the downstream face of the orifice plate andthe pipe diameter and the value selection of its conditions isas follows
119871
1015840
2
=
0 corner tappings
047 119863 and 119863
2
tappings254
119863
flange tappings
(10)
The uncertainty of the feedwater flow measured andcalculated by orifice plate and relevant equations will be givenin Section 32 The computer verification of this subroutinewill be integrated in Section 42
23 Single-Loop SCWR Program In single-loop type SCWRthe coolant is supercritical waterwhichwill be operated above
Pump
Reactor
Turbine
Condenser
Control rods
Figure 4 Sketch of SCWR with one loop
the critical point of water (119879119888= 647096K 119901
119888= 22064MPa)
The coolant remains single-phase when operated above thecritical point which is a stupendous advantage for it willeliminate coolant boiling throughout the systemTheno needfor recirculation results in the elimination of pressurizer jetpumps steam generators and steam separators This directcycle type is greatly simplified as shown in Figure 4
The thermal power in this type can be calculated withthermal balance using measured values including inlet andoutlet temperatures working pressure flow rate of coolantand the practical speed of pumpThe thermal power (119882)wasobtained by the following equation
119882 = 119876 times
Ω
Ω
0
times
(119867
ℎminus 119867
119888)
1000
(MW) (11)
where 119876 (kgs) is the flow rate of the coolant in the loopΩ (trmin) is the practical speed of pump Ω
0(trmin) is the
ideal speed of pump and 119867
ℎminus 119867
119888(kjkg) is the difference
between the enthalpy at the hot leg and the cold leg Theenthalpies are calculated using THPROP subroutine
24 Double-Loop SCWR Program Some conceptualdesigns of double-loop SCWR have been put forward likeCANDU-SCWR with a steam generator proposed by DrWilliam Fatoux [12] and a pressurized water reactor cooledwith supercritical water in the primary loop proposed byVogt et al [13] Double-loop SCWR drives a turbine bythe steams from the steam generator in the second loopindirectly as shown in Figure 5
Heat balance method in this type of SCWR is basedon the steam generator approximation enthalpy balance H-Power calculate the thermal power of reactor by the theoryof heat balance which obtains thermal power (of generator)in second loop from primary loop through the measurementvalues of temperature pressure and flow rate in the second
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
6 Science and Technology of Nuclear Installations
Pump
Reactor
Turbine
Condenser
Pressurizer Steam generator
Control rods
Figure 5 Sketch of SCWR with two loops
loop counting the internal heat loss in at the same time Theadvantages of the working conditions of second loop for easymeasurement makes it an important method of obtainingthermal power of the double-loop SCWR
Figure 6 shows the heat in and out the system (expressedby arrows) which can be described by the following heatbalance equation
119882
119877=
119873
sum
119894=1
119882SG119894
minus119882
ΔPr (12)
where the 119882119877is the core thermal power (MW) 119882SG
119894
is thethermal power obtained from the primary loop in the secondloop in 119894th steam generator and 119882
ΔPr is the thermal powercoolant system obtained from other heat sources (MW)which can be estimated from the design of reactor
The main physical process occurring in the steam gener-ator is as follows unsaturated water with the mass flow rate119876
119890and specific enthalpy 119867
119890flows into the steam generator
through the 119880 tube exchanges heat with the coolant inprimary loop and mostly becomes wet steam with the massflow 119876V and specific enthalpy 119867V after the increase ofendothermic enthalpy the others are the saturated blowdownwater with mass flow rate 119876
119901and specific enthalpy 119867
119901 The
thermal power in ith steam generator can be calculated withfollowing equation
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (13)
where119867V is thewet steam enthalpy in steam generator export119867
119901is the blowdown enthalpy119876
119901is the flow rate of blowdown
in second loop 119867119890is the feedwater enthalpy in second loop
and 119876119890is the flow rate of feedwater in second loop
The feed water satisfies the law of conservation of mass asfollows
119876
119890= 119876V + 119876119901 (14)
Simplify (13) and (14)
119882SG = (119867V minus 119867119890) 119876119890 minus (119867V minus 119867119901)119876119901 (15)
where feedwater enthalpy 119867
119890and blowdown enthalpy 119876
119901
are calculated by the thermodynamic properties subroutineflow rate of feedwater 119876
119890can be obtained from flow rate
calculation subroutine and the flow rate of blowdown 119876119901is
a measured valueThe wet steam always consists of saturated steam and
saturated water which is determined by vapour fraction 119909so the enthalpy of wet steam is characterized by the followingequation
119867V = 119909119867V119904 + (1 minus 119909)119867119897119904 (16)
where the 119867V119904 is the enthalpy of saturated steam and 119867
119897119904is
the enthalpy of saturated water both are calculated by thethermodynamic properties subroutine
3 Uncertainty Analysis of Double-Loop SCWR
The relative uncertainty of thermal power given in (17) isobtained by the uncertainty transmission formula
Δ119882
119882
= [
119899
sum
119894=1
[
119882SG119894119882
Δ119882SG119894119882SG119894
]
2
+ [
119882
ΔPr119882
Δ(119882
ΔPr)
119882
ΔPr]
2
]
12
(17)
where the Δ119882SG119894119882SG119894 is the uncertainty of thermal powerin steam generation in each second loop and Δ(119882
ΔPr)119882ΔPris the uncertainty of thermal power of coolant system inprimary loop
Δ119882SG119894Δ119882
le [
Δ119882SGΔ119882
]
119872
(18)
where [Δ119882SGΔ119882]
119872
is the max uncertainty of each steamgeneration
Assuming that
119882SG119894119882
=
1
119894
(19)
We can obtain the following equation
Δ119882
119882
=
1
119894
[
Δ119882SG119882SG
]
2
119872
+ [
119882
ΔPr119882
times
Δ119882
ΔPr119882
ΔPr]
2
12
(20)
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 7
Electric heater
Steamgenerator
Blowdown
Feedwater
Core heat production
Entranceheat loss
Pump
PumpChargingstream operation
streamLetdown
Reactor
Pressurizer
Figure 6 Heat balance principle diagram of double-loop SCWR
31 The Calculation of Δ119882119878119866119882
119878119866 The following equation
can be obtained by error propagation formula
Δ119882SG119882SG
=
[
[
[
[
[
[
[
119867V(119876119890 minus 119876119901)
119882SG
Δ119867V
119867V]
2
+ [
119867
119890119876
119890
119882SG
Δ119867
119890
119867
119890
]
2
+ [
119867
119901119876
119901
119882SG
Δ119867
119901
119867
119901
]
2
+[
119876
119890(119867V minus 119867119890)
119882SG
Δ119876
119890
119876
119890
]
2
+ [
119876
119901(119867V minus 119867119901)
119882SG
Δ119876
119901
119876
119901
]
2
]
]
]
]
]
]
12
Δ119867V
119867V= [[
119909
119867V(119867V119904 minus 119867119890119904)
Δ119909
119909
]
2
+ [
119867V119904
119867V119909
Δ119867V119904
119867V119904]
2
+[
119867
119890119904
119867V(1 minus 119909)
Δ119867
119890119904
119867
119890119904
]
2
]
12
(21)
Assume that the uncertainty of saturated water in the wetsteam is ldquo1rdquo as in (22) and inaccuracy of measurement shouldbe in this range
Δ (1 minus 119909)
1 minus 119909
=
119909
1 minus 119909
Δ119909
119909
= 1 (22)
Equation (22) can be deduced by the above formula
Δ119909
119909
=
1 minus 119909
119909
(23)
Δ119867V119904119867V119904 is the uncertainty of saturated steam enthalpymainly caused by the uncertainty of pressure measurementand water and steam thermodynamic properties as follows
Δ119867V119904
119867V119904= [(
Δ119867V119904
119867V119904)
2
119875V
+ (
Δ119867V119904
119867V119904)
2
119891
]
12
(24)
and the uncertainty caused by pressure measurement can becalculated by following equation
(
Δ119867V119904
119867V119904)
119875V
=
119875V
119867V119904
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597119867V119904
120597119875V
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119875V
119875V (25)
where Δ119875V is uncertainty caused by pressure measurementroot mean square of the uncertainty of pressure transmitterdata acquisition system and calibration determined by thedesign of pressure measurement
120597119867V119904
120597119875V= 120591119877119879
119904
43
sum
119894=1
119899
119894119869
119894(120591 minus 05)
119869119894minus1
119868
119894(
01119875V
119901
lowast
)
119868119894minus1
(
1
119901
lowast
)
(26)
where 119868
119894 119869
119894 119899
119894is given in IAPWS-IF97 and 120587 =
01119875V119901lowast
120591 = 119879
lowast
119905119890 119901
lowast
= 1MPa 119879lowast = 540K and119877 = 0461526 kJ kgminus1Kminus1
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
8 Science and Technology of Nuclear Installations
(Δ119867V119904119867V119904)2
119891
is the uncertainty caused by the calculationof water and steam thermodynamic properties where Δ119867V119904can be selected in the corresponding section of IAPWS-IF97
32 The Calculation of Δ119867119890119904119867
119890119904 The uncertainty of sat-
urated water enthalpy Δ119867
119890119904119867
119890119904and feedwater enthalpy
Δ119867
119890119867
119890can be estimated by the method the same as
Δ119867V119904119867V119904mentioned aboveThe relative uncertainty of mass flow rate 120575119902
119898119902
119898can be
described by the following equation
120575119902
119898
119902
119898
= ((
120575119862
119862
)
2
+ (
120575120576
120576
)
2
+ (
2120573
4
1 minus 120573
4
)
2
(
120575119863
119863
)
2
+(
2
1 minus 120573
4
)
2
(
120575119889
119889
)
2
+
1
4
(
120575Δ119901
Δ119901
)
2
+
1
4
(
120575120588
1
120588
1
)
2
)
12
(27)
The uncertainty of discharge coefficient is given by
119862 =
(07 minus 120573) 01 le 120573 le 02
05 02 le 120573 le 06
(1667120573 minus 05) 06 le 120573 le 075
(28)
If119863 lt 7112mm (10) should add the following term
09 (075 minus 120573) (28 minus
119863
254
) (29)
If 120573 gt 05 and Re119863lt 10000 the above values should add
the following relative uncertainty
+05 (30)
The uncertainty of expansibility factor 120576 is 35(Δ1199011205811199011)
for compressible fluid 120576 = 0The uncertainty of internal diameter of the pipe line can
be estimated by the following equation
120590
119863=
005 times 119889
119894
times 2
radic3
= 005 times 119889
119894
times 115 (31)
where 005times119889119894 is the error of themeasuring instrument ldquo2rdquois an extension coefficient of the confidence interval of 95radic3 is the constant of rectangular distributionThe volume elasticity coefficient of water is quite large
determining that its compressibility is very small so theinfluence of pressure on the density can be ignored Theuncertainty of feed water density 120590120588120588 is determined by theuncertainty of temperature measurement and the calculationof water properties as follows
(
Δ120588
120588
) = [(
Δ120588
120588
)
2
119905119890
+ (
Δ120588
120588
)
2
119891
]
12
(32)
and the uncertainty caused by temperature measurement canbe calculated by following equation
(
Δ120588
120588
)
119905119890
=
119905119890
120588
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
120597120588
120597119905119890
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
Δ119905119890
119905119890
(33)
Table 2 The main parameters reference design of the US SCWR
Parameter ValueThermal power 3575MWthOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 510sim550∘CReactor mass flow rate 1843 kgs
Table 3 The input and output values calculated by H-Power
Input parameter ValueOperating pressure 25MPaReactor inlet temperature 280∘CReactor outlet temperature 520∘CReactor mass flow rate 1843 kgsIdeal pump speed 1900 trminPractical pump speed 1850 trminOutput parameter ValueCold leg enthalpy 12302407 kjkgHot leg enthalpy 32164985 kjkgThermal power 35643396MW
Thecalculation procedures andmethod of the parametersare the same as the Δ119867V119867V mentioned above
The relative uncertainty of Δ(119882ΔPr)119882ΔPr is estimated by
experience values
4 Validation of H-Power Code
41 Single-Loop Type Program We have done the verificationof single-loop program in H-Power using the main parame-ters design by Jacopo Buongiorno as in Table 2 and assumingthe ideal and practical pump speed according to the level ofpump speed at present
The calculation result of thermal power 35643396MWgiven in Table 3 shows a high consistency with the value3575MW designed by US in Table 3
42 Double-Loop SCWR Program Due to the lack of designdata of SCWR the validation of this part has been done byusing the values of Qinshan Phase II [13] in Table 4 thoughit is not SCWR Table 5 shows the comparison between theresults of H-Power and the values of Qinshan Phase II
Although the main calculation result trend of SCWR issame as CNP650 of Qinshan Phase II there is many detaildifferences in thermodynamic properties of water and steamand uncertainties calculation The inconsistencies in Table 5also come from the different input parameters in measuringinstrument
It is a valid way to verify the H-Power while the maincalculation process of both PWR and SCWR is the same andthere is no particular data of SCWR fitting for the code Theresult in Table 5 shows that H-Power runs well and has a validtrend in thermal power and its relevance computation So itcan be used in SCWR design and calculation
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 9
Table 4 Input parameters of H-Power using the values of Qinshan Phase II
Parameters ValuesOrifice diameter in reference (m) 02417Feedwater pipe diameter in reference (m) 036374Steam pipe diameter in reference (m) 0739Orifice linear expansion coefficient (mm∘C) 00000166Feedwater pipe linear expansion coefficient (mm∘C) 00000121Steam pipe linear expansion coefficient (mm∘C) 00000121Orifice reference temperature (∘C) 20Feedwater pipe reference temperature (∘C) 20Steam pipe reference temperature (∘C) 20Feedwater pressure difference (KPa) 1821147Feedwater temperature (∘C) 228920334Feedwater pressure (MPa) 711855Steam pressure (MPa) 6941479Blowdown flow rate (th) 20757261
Table 5 Comparison between the results of the values of Qinshan Phase II and H-Power
Parameters Qinshan Phase II H-PowerFeedwater density (kgm3) 83312894 83269758Feedwater enthalpy (kjkg) 98618622 98607354Saturated water enthalpy (kjkg) 12643947 12655310Saturated steam enthalpy (kjkg) 27741882 27730492Steam enthalpy (kjkg) 27726784 27715417Blowdown enthalpy (kjkg) 12643947 1265531Discharge coefficient 0603068 0606047Feedwater flow rate (th) 19484789 19576866Generator thermal power (MW) 9582318 97094089Feedwater flow rate uncertainty 0007236 0006088
5 Conclusions
The thermal power calculation code H-Power for SCWRwas developed based on heat balance method which canbe easily applied in designs and operation In this paperthermodynamic properties calculation subroutine based onIAPWS-IF97 has been verified and the uncertainty analysishas been proposed The validation of H-Power has beencarried out in two parts single-loop SCWR by the data givenby Jacopo Buongiorno and double-loop SCWR by the valuesof Qinshan Phase II Although Qinshan Phase II is a PWRthe result can show that H-Power is valid because the maincalculation process of both PWR and SCWR is the same Inthe future the validation will be carried out using the valuesof SCWR when published
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] K Dobashi Y Oka and S Koshizuka ldquoConceptual design ofa high temperature power reactor cooled and moderated bysupercritical light waterrdquo in Proceedings of the 6th InternationalConference on Nuclear Engineering (ICONE6 rsquo98) San DiegoCalif USA 1998
[2] S Shijia ldquoCalculation analysis of the heat balance test of l LingAo Nuclear Power Plant core powerrdquo Chinese Journal of NuclearScience and Engineering vol 25 pp 271ndash277 2005
[3] X Yang G H Su W Tian J Wang and S Qiu ldquoNumericalstudy on flow and heat transfer characteristics in the rod bundlechannels under super critical pressure conditionrdquo Annals ofNuclear Energy vol 37 no 12 pp 1723ndash1734 2010
[4] X J Liu and X Cheng ldquoThermal-hydraulic and neutron-physical characteristics of a new SCWR fuel assemblyrdquo Annalsof Nuclear Energy vol 36 no 1 pp 28ndash36 2009
[5] T Reiss G Csom S Feher and S Czifrus ldquoThe simplifiedsupercritical water-cooled reactor (SSCWR) a new SCWRdesignrdquo Progress in Nuclear Energy vol 52 no 2 pp 177ndash1892010
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
10 Science and Technology of Nuclear Installations
[6] B Jacopo ldquoProgress report for the FY-03 generation-IV RampDactivities for the development of the SCWR in the USrdquo USINEEL EXT-03-01210 2003
[7] Y Guodong and P Zefei ldquoThe analysis of qinshan secondnuclear power plant power calibration methodrdquo in Proceedingsof the 12th Reactor Numerical Calculation and Particle TransportAcademic Conference Anhui China 2008
[8] The International Association for the Properties of Water andSteam ldquoRelease on the IAPWS industrial formulation 1997 forthe thermodynamic properties of water and steamrdquo Germany1997
[9] The 1967 IFC formulation for Industrial use unrestrictedpublication allowed in all countries
[10] P-H Wang J-Y Jia and M-H Cheng ldquoThe calculatingmodels of water and steam properties with IAPWS-IF97rdquo PowerEngineering vol 20 no 6 pp 988ndash991 2000
[11] ISO 5167 ldquoMeasurement of fluid flow by means of pressuredifferential devices inserted in circular cross-section conduitsrunning fullmdashpart 2 orifice platerdquo 2003
[12] William Fatoux ldquoA CANDU-SCWR with a steam generatorpreliminary thermodynamic assesment and estimation of foul-ing ratesrdquo 2009
[13] B Vogt K Fischer J Starflinger E Laurien andT SchulenbergldquoConcept of a pressurized water reactor cooled with supercriti-cal water in the primary looprdquo Nuclear Engineering and Designvol 240 no 10 pp 2789ndash2799 2010
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Research ArticleA Simplified Supercritical Fast Reactor with Thorium Fuel
Peng Zhang12 Kan Wang1 and Ganglin Yu1
1 Department of Engineering Physics Tsinghua University Beijing 100084 China2 School of Power and Mechanical Engineering Wuhan University Wuhan 430072 China
Correspondence should be addressed to Peng Zhang zhangpeng03gmailcom
Received 6 December 2013 Revised 21 January 2014 Accepted 22 January 2014 Published 10 March 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Peng Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Super-Critical water-cooled Fast Reactor (SCFR) is a feasible option for the Gen-IV SCWR designs in which much less moderatorand thus coolant are needed for transferring the fission heat from the core compared with the traditional LWRsThe fast spectrumof SCFR is useful for fuel breeding and thorium utilization which is then beneficial for enhancing the sustainability of the nuclearfuel cycle A SCFR core is constructed in this work with the aim of simplifying the mechanical structure and keeping negativecoolant void reactivity during the whole core life A core burnup simulation scheme based on Monte Carlo lattice homogenizationis adopted in this study and the reactor physics analysis has been performed with DU-MOX and Th-MOX fuel The main issuesdiscussed include the fuel conversion ratio and the coolant void reactivity The analysis shows that thorium-based fuel can provideinherent safety for SCFR without use of blanket which is favorable for the mechanical design of SCFR
1 SCFR Conceptual Design
In SCWR much less coolant water is needed for cooling thereactor so a fast spectrum option (SCFR) is possible With aharder spectrum SCFR can have a higher conversion ratioThus physically SCFR is a kind of high conversion LWRdesign for which the main approach to increase conversionratio is to decrease the ratio of water to heavy metal so asto decrease the moderation effect of water and make thespectrum hard [1ndash4]
The coolant void reactivity (CVR) is a crucial safety aspectof fast reactor design Main concern arising from coolantvoiding is the hardening of the neutron spectrum whichincreases fast fission in both seed and blanket fuel regionsand also increases neutron leakage at the same time In orderto decrease the CVR the flat core design is usually adoptedto increase the neutron leakage But it is not an economicaloption for SCFR since it is operated at a very high pressureand so a bigger and thicker pressure vessel is needed tocontain the coreThus increasing neutron absorption at voidcondition is the key for achieving negative CVR in SCFR andso blankets are very important since they are the only regionsin the core where neutron capture strongly prevails overfission A typical SCFR blanket design is shown in Figure 1 in
which a ZrH layer is adopted to slow down the fast neutronleaked from seed assemblies at void condition and decreasethe fast fission at blanket assemblies [5ndash8]
However in SCFR the coolant in blanket assembly is verycold as very little heat generated so the flow channels shouldbe separated from those of the seed assembliesThiswillmakethe flow path and the core mechanical design complicatedIn order to simplify the mechanical design we need to thinkout another way to keep CVR negative Introducing thoriumfuel is a possible option [4 9ndash11] so this paper work mainlyfocuses on it
A SCFR core conceptual design is proposed as shown inFigure 2 No blanket assembly is adopted in the design Thecore power density will increase in this case since a blanketassembly has much lower power than a seed assembly andthe mechanical design can be simplified as it is not neededto separate coolant flow in blanket and seed assemblies Inaddition it is possible to achieve negative CVR by changingthe fuel design such as thorium fuel which is a main purposeof this work
The SCFR core can be divided into two radial regions theinner core and the outer core The numbers of assemblies forthe two parts are generally the same The inlet coolant flowsdownwards through outer core assemblies first After mixing
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 405654 9 pageshttpdxdoiorg1011552014405654
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
2 Science and Technology of Nuclear Installations
Fuel rod
Stainless steel12060170mm
ZrH layer
11 cm
255 cm
Blanket assembly
Figure 1 A typical SCFR blanket assembly design
Table 1 SCFR core design parameters
Parameters ValueNumber of assembly 241 (inner 121 outer 120)Equivalent diameterm 297Active lengthm 36Thermal powerMWt 3498Electric powerMWe 1532Average linear heat generationratekWm 16
Average power densityMWm3 140
Table 2 SCFR assembly design parameters
Parameters ValuePellet ODmm 82Cladding ODmm 962Cladding thicknessmm 063
Cladding materialMA956 Fe-215Cr-575Al-
06Ti-07Y2O3725 gcm3
Pitchmm 1062119875D 11Pin-to-channel-box gapmm 05Channel box thicknessmm 25Gap between adjacent channelboxmm 10
Assembly widthmm 1822
in the lower plenum the coolant flows upwards throughthe inner core assemblies to the upper plenum and then tothe outlet The main design parameters of SCFR core andassembly are listed in Tables 1 and 2
Table 3 The different fuel forms chosen for study
Fuel type Fuel composition Enrichment definitionDU-MOX RGPuO2 + DUO2 (239Pu + 241Pu)HMTh-MOX RGPuO2 +ThO2 (239Pu + 241Pu)HM
Table 4 SCFR core parameters with different fuel options
Parameters Th-MOX ThMOX +MOXFuel forms
Inner (RGPu +Th)O2 (RGPu +Th)O2
Outer (RGPu +Th)O2 (RGPu + DU)O2
EnrichmentInner 85 85Outer 75 60
Batch numberInner 3 3Outer 4 5
Core 119896eff (0sim550 EFPDs) 1031sim1049 1030sim1050Maximum PPF 148 198Average dischargeburnupMWdkgHM
Inner 572 684Outer 710 645Whole core 629 670
Maximum dischargeburnupMWdkgHM
Inner 611 760Outer 742 718
FIRInner 101 101Outer 081 101Whole core 093 101
2 The lsquolsquoTwo-Steprsquorsquo MC Core BurnupAnalysis Method
MonteCarlomethod has beenwidely used for the verificationand validation of deterministic codes and also for the analysisof many newly developed nuclear energy systems since itcan deal with arbitrary geometry and spectrum configuration[12] However the efficiency of Monte Carlo calculation istoo low for the ordinary large scale core designs due to thelong simulation time to get reliable results With the rapiddeveloping of computer technologies and parallel algorithmsthe efficiency of Monte Carlo simulation has been greatlyincreased Coupled neutronic thermal-hydraulic analysis offull core with Monte Carlo has been done [13] but coreburnup analysis with continuous energy Monte Carlo is stilldifficult nowadays
A ldquotwo-steprdquo Monte Carlo core burnup analysis methodis proposed in this work Similar to the deterministic codesystems the core calculation scheme is divided into two stepsFirst the assembly simulation is donewith continuous energy
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 3
Assemblies with downward flow
Assemblies with upward flow
25mm
1822
mm1 2
222
2 23
33
3
3 3
4
44
4
4 4
5 6 7 8
56
78
9
9
56
78
56789
9
56
78
9
56
78
9
Figure 2 Conceptual design of SCFR core and assembly
Initialize materialcomposition and burnup
information
Run ORIGENto half-step
Run ORIGENto full-step
Run MCNP CE
Update burnup step
All burnup stepsfinished
Finish assembly burnupsimulation
Yes
No
Get burnup-dependent cross
sections
Cross-sectionparameterization
module
RunMCNP MG
Powerdistribution
Update burnupdistribution
All burnup stepsfinished
Refuelingfinished
Finish core burnupsimulation
Yes
Yes
No
No
MCBurn MCCBurn
Figure 3 Two-step Monte Carlo core burnup analysis system
Monte Carlo and the assembly group cross-sections aretallied at the same time Second with these group constantsthe core simulation is done with multigroup Monte Carlo[14] which can greatly increase the core simulation efficiencyThe core burnup analysis can be done if the assembly groupconstants can be prepared for different burnup states
The ldquotwo-steprdquo core simulation scheme is illustrated inFigure 3 MCBurn a coupling code of MCNP CE (contin-uous energy mode of MCNP) and ORIGEN is adoptedfor assembly burnup simulations [15] The assembly groupconstants are gathered and organized to prepare group cross-sections for core calculations MCCBurn code is developed
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
4 Science and Technology of Nuclear Installations
06
07
08
09
1
11
12
13
14
15
kin
f(D
M=03
gcc
)
0 20000 40000 60000 80000
Burnup (MWDtU)
minus1
minus08
minus06
minus04
minus02
0
02
04
06
08
1
err (
)
kinf MCBurnkinf MCCBurn G2P1Err ()
Figure 4 A BWR assembly model and its burnup calculation results
0
0005
001
0015
002
0025
003
Flux
1E minus 09 00000001 000001 0001 01 10 1000
Energy (MeV)
Inner coreOuter core
PWRSFR
Figure 5 Spectrum comparison of SCFR (inner and outer core) PWR and SFR
to manage core burnup simulation which uses MCNP MG(multigroup mode of MCNP) to do core criticality simula-tions
In order to justify the calculation tools a BWR assemblywith moderator density (DM) 03 gcm3 has been modeledusing MCBurn and MCCBurn with KCODE card of MCNPas ldquoKCODE 5000 10 30 90rdquo The burnup calculation resultsare shown in Figure 4 It can be seen that the differences of119896inf between MCBurn and MCCBurn are well below 02which reveals that the group cross-sections generated usingour method is right
3 Reactor Physics Characteristics of SCFRwith DU-MOX and Th-MOX
In order to concentrate on the reactor physics characteristicsanalysis of SCFR the thermal-hydraulic parameters havebeen simplifiedThe coolant densities of inner and outer coreare set to be the average values along core height 013 gcm3
and 06 gcm3 respectively Besides a pin cell is modeled torepresent the assembly whichmeans the radial heterogeneityof assembly is ignoredThis may introduce some errors to theresults but we think this can be neglected for the preliminaryfeasibility study
We have chosen DU-MOX and Th-MOX for the com-paring study which are listed in Table 3 The isotope weightvector of reactor grade plutonium (RGPu) is as follows 28238Pu 544 239Pu 228 240Pu 118 241Pu 7 242Pu and12 241Am The depleted uranium (DU) is assumed to have025 weight 235U
31 Spectrum Comparison Supposing the fuel is DU-MOXwith an enrichment of 75 the inner and outer corespectrums are shown in Figure 5 The spectrums of PWRand sodium-cooled Fast Reactor (SFR) are also included forcomparison It can be seen that there is no PWR-like thermalpeak for SCFRrsquos spectrum Spectrum of inner core is harderthan outer core since the coolant density is lower
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 5
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
1
105
11
115
12
125
kin
f
minus60
minus40
minus20
0
20
40
CVR
(pcm
vo
id)
08
09
1
11
12
13
14
CR
08
09
1
11
12
13
FIR
fis Pu = 6fis Pu = 75fis Pu = 9
Figure 6 Inner cell burnup performances with DU-MOX fuel
fis Pu = 6fis Pu = 75fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0
0
20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
09
095
1
105
11
115
12
125
kin
f
07
08
09
1
11
CR
minus80
minus60
minus40
minus20
20
40
60
80
CVR
(pcm
vo
id)
08
085
09
095
1
105
FIR
Figure 7 Outer cell burnup performances with DU-MOX fuel
32 Cell Burnup Performance
321 DU-MOX Fuel Cell Themain burnup performances ofinner and outer cells with different enrichments are shown inFigures 6 and 7 Where CVR is the coolant void reactivityCR conversion ratio is defined as the ratio of capture rate offertile nuclides (232Th 238U 238Pu and 240Pu) to absorption
rate of fissile nuclides (233U 235U 239Pu and 241Pu) and FIRfissile inventory ratio is defined as the ratio of total amountof fissile material to the initial loading fissile material
From these figures we can see that the cell burnup perfor-mances are sensitive to fuel enrichment With the increasingof fuel enrichment cell initial 119896inf increases notably and thedifferences decrease with burnup CVR goes positive rapidly
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
6 Science and Technology of Nuclear Installations
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)
08
09
1
11
12
kin
f
minus120
minus100
minus80
minus60
minus40
minus20
0
20
CVR
(pcm
vo
id)
08
1
12
14
16
CR
09
1
11
12
13
14
FIR
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
Figure 8 Inner cell burnup performances with Th-MOX fuel
fis Pu = 6fis Pu = 75
fis Pu = 85fis Pu = 9
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
0 20000 40000 60000 80000 100000
Burnup (MWDtU)0 20000 40000 60000 80000 100000
Burnup (MWDtU)
095
1
105
11
115
kin
f
075
08
085
09
095
1
105
CR
minus300
minus250
minus200
minus150
minus100
minus50
0
CVR
(pcm
vo
id)
065
075
085
095
105
FIR
Figure 9 Outer cell burnup performances with Th-MOX fuel
and it increases slowly with burnup CR and FIR decreasessignificantly
322 Th-MOX Fuel Cell TheTh-MOX fuel cell burnup per-formances for inner and outer core are shown in Figures 8 and9 The same trends can be observed for the parameters whenfuel enrichment and burnup changed A great advantage ofadopting thorium fuel is that the CVR of cell can be kept
negative for a wide range of enrichment and for the wholelife cycle Considering the negative effect of neutron leakagethe CVR of SCFR core will be negative So in the followingcore analyses CVR is not discussed in detail
Thus thorium fuel is very suitable for SCFR and Th-MOX is adopted in the following study Considering thecritical ability the fuel enrichment for inner and outer coreis chosen as 85 and 75 respectively
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 7
52
1010
40
20
20
3050
6030
71
62
80
81
11
51
22
91
102
70
21
72
90
92
31
41
32
100
101
103
71
61
12
110
82
93
62
42
120
111
123
80
121
122
113
81
11283
83
(a) Inner 3-batch outer 4-batch
52
1010
40
20
20
3050
6030
71
62
81
83
11
51
22
91
93
70
21
72
80
82
31
41
32
90
92
94
71
61
12
100
111
84
62
42
110
102
114
81
101
112
104
83
103113
113
(b) Inner 3-batch outer 5-batch
Figure 10 Core loading scheme (mn mmdashthe assembly group number nmdashcycles of the assembly has been burned)
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 100 200 300 400 500 600
EFPD
1
11
12
13
14
15
16
PPF
C7simC12 average
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud ave inBud ave outBud ave
Bud max outBud max in
Figure 11 Multicycle burnup simulation results for Th-MOX core
33 Core Burnup Performance
331 Core Loading Pattern In order to get the equivalent fuelcycle performances we need to design the fuel loading pat-ternsThe inner and outer core are considered independentlysince they have different reactor physics characteristics
Assuming that the average linear heat generation rateis 16 kWm the specific power density should be about34 kWkgHM The object burnup is supposed to be 60sim70MWdkgHM so an assembly should stay in core for 1800sim2000 days and loading pattern can be 3- 4- or 5-batchloading pattern In this work the cycle length is fixed as 550
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
8 Science and Technology of Nuclear Installations
keff C1keff C2keff C3keff C4keff C5keff C6
keff C7keff C8keff C9keff C10keff C11keff C12
0 5000 10000 15000 20000 25000 30000
Burnup (MWDtU)
0
102
104
106
108
keff
0 100 200 300 400 500 600
EFPD
C7simC12 average
0
12
14
16
18
2
22
PPF
0 2 4 6 8 10 12 14
Cycle0 2 4 6 8 10 12 14
Cycle
Bud ave inBud ave outBud ave
0
20000
40000
60000
80000
Burn
up (M
Wd
tHM
)
0
20000
40000
60000
100000
80000
Burn
up (M
Wd
tHM
)
Bud max inBud max out
Figure 12 Multicycle burnup simulation results for Th-MOX+DU-MOX core
days Considering the higher power density of inner core 3-batch loading pattern is suitable for inner core while 4- or5-batch loading pattern for outer core The loading schemesfor 16 symmetric core are shown in Figure 10
332 Multicycle Simulation The multicycle core simulationresults are shown in Figure 11 The in-3-out-4 batch loadingpattern is adopted PPF (peak power factor) is the ratio ofthemaximumassembly power to the average assembly powerThe 119896eff of core increases slowly with burnupThe average andmaximum discharge burnups of inner core (57MWdkgHMand 61MWdkgHM) are lower than that of the outer core(71MWdsdotkgHM and 74MWdkgHM)
Since the inner and outer core regions are not coupledtightly the fuel forms can be different for the two regionsConsidering the CVR DU-MOX should not be loadedin the inner region since the cell burnup results indicatethat local CVR may be positive at a burnup higher than40GWdtHM Considering that many neutrons may leakfrom the core at void condition it is possible to load DU-MOX fuel in the outer region while still keeping a negativeCVR for the whole core Th-MOX fuel is loaded in the innerregionThe enrichments forTh-MOXandDU-MOXare 85
and 6 In-3-out-5 batch loading pattern is adopted and themulticycle core simulation results are shown in Figure 12Thedifference of discharge burnups between inner and outer coreregion is decreased The main core parameters at equivalentcycle are listed in Table 4
4 Conclusion
In this work a SCFR core conceptual design is proposedThe core can be divided into two radial regions the innerregion and the outer regionThe spectrums of the two regionsare different which results in their different reactor physicscharacteristics The fuel forms and the loading patterns ofthe two regions can be designed independently Unlike thesignificant 119896eff decrease in the traditional LWRs the 119896eff of theproposed SCFR core increases slowly during the whole lifecycleThis reveals that SCFR has good fuel conversion abilityWith the adoption of thorium fuel the CVR can be keptnegative during the whole life cycle without use of blanketwhich is also beneficial for increasing the power density andsimplifying the mechanical design
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 9
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was sponsored by the National Basic ResearchProgram of China (2007CB209800) and the National NaturalScience Foundation of China (Approved no 11305036)
References
[1] Y Oka T Jevremovic and S Koshizuka ldquoA direct-cyclesupercritical-water-cooled fast breeder reactorrdquo Journal ofNuclear Science and Technology vol 31 no 1 pp 83ndash85 1994
[2] Y Ishiwatari Y Oka and S Koshizuka ldquoBreeding ratio analysisof a fast reactor cooled by supercritical light waterrdquo Journal ofNuclear Science and Technology vol 38 no 9 pp 703ndash710 2001
[3] S Uchikawa T Okubo T Kugo et al ldquoConceptual designof innovative water reactor for Flexible Fuel Cycle (FLWR)and its recycle characteristicsrdquo Journal of Nuclear Science andTechnology vol 44 no 3 pp 277ndash284 2007
[4] Z Peng Research on the reactor physics analysis methods andcharacteristics of supercritical water-cooled reactor [PhD thesis]Tsinghua University 2012 (Chinese)
[5] Y Oka and T Jevremovic ldquoNegative coolant void reactivity inlarge fast breeder reactors with hydrogenous moderator layerrdquoAnnals of Nuclear Energy vol 23 no 14 pp 1105ndash1115 1996
[6] J Yo Y Ishiwatari Y Oka et al ldquoComposite core design ofhigh power density supercritical water cooled fast reactorrdquoProceedings of the GLOBAL Tsukuba Japan 2005
[7] L Cao Y Oka Y Ishiwatari and Z Shang ldquoFuel core designand subchannel analysis of a superfast reactorrdquo Journal ofNuclear Science and Technology vol 45 no 2 pp 138ndash148 2008
[8] L Cao Y Oka Y Ishiwatari and S Ikejiri ldquoThree-dimensionalcore analysis on a super fast reactor with negative local voidreactivityrdquo Nuclear Engineering and Design vol 239 no 2 pp408ndash417 2009
[9] International Atomic Energy Agency ldquoThorium fuel cyclemdashpotential benefits and challengesrdquo Tech Rep IAEA-TECDOC-1450 2005
[10] S Permana N Takaki and H Sekimoto ldquoBreeding and voidreactivity analysis on heavy metal closed-cycle water cooledthorium reactorrdquo Annals of Nuclear Energy vol 38 no 2-3 pp337ndash347 2011
[11] V Jagannathan and U Pal ldquoTowards an intrinsically safe andeconomic thorium breeder reactorrdquo Energy Conversion andManagement vol 47 no 17 pp 2781ndash2793 2006
[12] X-5 Monte Carlo Team ldquoMCNPmdasha general Monte Carlo N-particle transport code version 5rdquo Tech Rep LA-CP-03-0284Los Alamos National Laboratory 2003
[13] D Kotlyar Y Shaposhnik E Fridman and E ShwagerausldquoCoupled neutronic thermo-hydraulic analysis of full PWRcorewith Monte-Carlo based BGCore systemrdquo Nuclear Engineeringand Design vol 241 no 9 pp 3777ndash3786 2011
[14] J C Wagner E L Redmond S P Palmtag and J S HendricksldquoMCNP multigroupadjoint capabilitiesrdquo Tech Rep LA-12704Los Alamos National Laboratory 1994
[15] Y Ganglin W Kan and W Yuhong ldquoMCBurnmdasha couplingpackage of program MCNP and ORIGENrdquo Atomic EnergyScience and Technology vol 37 no 3 pp 250ndash254 2003
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Research ArticleExperimental Investigation on Flow-Induced Vibration of FuelRods in Supercritical Water Loop
Licun Wu Daogang Lu and Yu Liu
Nuclear Science and Engineering North China Electric Power University Beijing 102206 China
Correspondence should be addressed to Licun Wu wlc121126com
Received 10 November 2013 Revised 15 January 2014 Accepted 15 January 2014 Published 24 February 2014
Academic Editor Jiejin Cai
Copyright copy 2014 Licun Wu et alThis is an open access article distributed under theCreativeCommonsAttributionLicense whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The supercritical water-cooled reactor (SCWR) is one of the most promising Generation IV reactors In order to make the fuelqualification test for SCWR a research plan is proposed to test a small scale fuel assembly in a supercritical water loop To ensurethe structure safety of fuel assembly in the loop a flow-induced vibration experiment was carried out to investigate the vibrationbehavior of fuel rods especially the vibration caused by leakage flow From the experiment result it can be found that the vibrationof rods is mainly caused by turbulence when flow rate is low However the effects of leakage flow become obvious as flow rateincreases which could changes the distribution of vibrational energy in spectrum increasing the vibrational energy in high-frequency band That is detrimental to the structure safety of fuel rods Therefore it is more reasonable to improve the designby using the spacers with blind hole which can eliminate the leakage flow to assemble the fuel rods in supercritical water loopOn the other hand the experimental result could provide a benchmark for the theoretical studies to validate the applicability ofboundary condition set for the leakage-flow-induced vibration
1 Introduction
The supercritical water reactor is a Generation IV reactorconcept which uses supercritical water as the working fluidThe high thermodynamic efficiency and plant simplificationmake SCWR attractive for consideration as a promisingadvanced nuclear system In order to develop a viable designfor the core accurately estimate the heat transfer coefficientand develop materials for the fuel and core structure thatwill be sufficiently corrosion-resistant to withstand SCWRconditions a research plan which is made by the steeringcommittee of the SCWR system in the Generation IVInternational Forum is proposed to test a small scale fuelassembly in a supercritical water loop in the LVR-15 researchreactor which is located in Nuclear Research Institute in RezCzech Republic This water cooled reactor with an enoughcore height enables replacing one of its assemblies with apressure tube containing four fuel rods as Figure 1 showsThese four fuel rods can reach a fissile power of more than50 kW A recuperator inside the pressure tube situated rightabove the fuel rods is boosting the feed-water temperature
of 300∘C to typical evaporator conditions A cooler in thetop section of the pressure tube acts as the heat sink toremove the fissile and gamma power The pressure tube willbe connected with coolant pumps and safety and auxiliarysystems forming the supercritical water loop to simulate asupercritical water environment at the fuel assembly whilethe rest of the core operates at ambient pressure (Figure 2)Before carrying out the project a series of safety analyseson the small scale fuel assembly will be made including theexperimental investigation on the flow-induced vibration offuel assembly which is presented in this paper
In general there is a tiny clearance between the fuel rodand the spacer tomake charging easier and the wear betweenthe fuel rods and spacer will make the clearance becomelarger over time Consequently the fuel rods would vibratein case of coolant flowing through the narrow clearanceThisphenomenon is called leakage-flow-induced vibration whichhas been studied by many researchers (Blevins [1] Hobson[2] Chen [3]) Paıdoussis [4] wrote a review to introducesome serious accidents in the nuclear reactors caused by it
Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 769432 9 pageshttpdxdoiorg1011552014769432
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
2 Science and Technology of Nuclear Installations
R145 R17
R285
Pressure tube
Guidetubes
Fuelrods
Assembly box
OutletInletCooler
Recuperator
Test sectionwith 4 fuel rods
Figure 1 Concept of the active channel for SCWR fuel qualification
Low pressurecoolant injection
Recir-culationpump
Emergency pump
Depressurizationsystem
Pressurizerand
accumulator
Primary pump
Accumulator
Reactor building
Cooler
Fuel
rods
120574-po
wer
Active channel
Figure 2 Schematic diagram of the primary loop and of the safetysystem for the SCWR fuel qualification test
Mateescu and Paidoussis [5] researched the unsteadypotential flow in a narrow annular passage which is formedby a motionless rigid duct and an oscillating rigid center-body both of axially variable cross-sections The fluiddynamic force exerted on the center-body was obtained onthe basis of unsteady potential flow theory It was concludedthat the stability of center-body decreases as the pivot ofrotation is shifted towards the downstream end of the center-body and a divergent annular passage has a destabilizingeffect Arai and Tajima [6] studied a similar problem by usinga different approach
Li et al [7] developed a numerical method to analyze theflutter instability of the flow vibration of the inner cylinderMeanwhile an experiment on the annular leakage-flow-induced vibration was carried out and a critical flow rateof the flutter instability was obtained for several annularleakage-flow systems with different passage increment ratiosas well as the eccentricities They found that a divergentannular passage may cause a negative fluid damping so the
flutter instability will happen when the flow rate is larger thanthe critical flow rate
Langthjem et al [8] investigated the linear stability of aflexible cylindrical rod exposed in annular leakage flow It isfound that when flow speed reaches a certain critical valuesimply supported rods may become unstable by either flutteror divergence
Fujita et al [9] investigated the dynamical behavior ofan axisymmetric elastic beam subjected to axial leakageflow By making complex eigenvalue analysis the variationof the dynamic behavior during pre- and postinstabilityis researched with respect to increasing axial leakage-flowvelocity The relationships between the unstable phenomenaand axial flow velocities are clarified for the transition fromthe lower mode to higher mode
Since the study on leakage-flow-induced vibration of thefuel rods has not been reported previously and the stabilityassociatedwith the leakage flowmechanism strongly dependson the detailed geometries and fixed mode of the structureit is necessary to perform an experiment to investigate theeffects of leakage flow on the vibration of the small scale fuelrods in supercritical water loop The present research is anextension of previous studies and aims at investigating thevibration characteristics of fuel rods under the influence ofleakage flow On one hand the experimental results couldprovide a reference for optimal design of the fuel assemblyin supercritical water loop On the other hand it couldbe treated as the benchmark to validate the availabilityof mathematical model built for the leakage-flow-inducedvibration
2 Theoretical Models
Consider a circular fuel rod immersed in the coolant flowingat velocity119880 parallel to the 119911 axis (Figure 3) The fuel rod hasflexural rigidity 119864119868 linear density (mass per unit length) 119898and total length 119897 All motions of the fuel rod are assumed tobe confined in the119910-119911 plane According to the studies of Chen[3] the equation of motion is written as
119864119868
120597
4
119906
120597119911
4
+ 120578119868
120597
5
119906
120597119905120597119911
4
+ 119898
119886119880
2120597
2
119906
120597119911
2
minus 120574119879
0
120597
2
119906
120597119911
2
minus
1
2
119862
119879
119898
119886119880
2
119863
[(1 minus
1
2
120574) 119897 minus 119911]
120597
2
119906
120597119911
2
minus
1
2
(1 minus 120574)119862
1015840
119879
119898
119886119880
2120597
2
119906
120597119911
2
+ 2119898
119886119880
120597
2
119906
120597119911120597119905
+
1
2
119862
119873
119898
119886119880
2
119863
120597119906
120597119911
+
1
2
119862
119873
119898
119886119880
119863
120597119906
120597119905
+ 119862
119881
120597119906
120597119905
+ (119898 + 119898
119886)
120597
2
119906
120597119905
2
= 119892 (119909 119905)
(1)
where 119906 is the displacement of fuel rod 119864 is the modulus ofelasticity119898
119886is the added mass 119879
0is the initial axial tension
119862
1015840
119879
is the form drag coefficient at the free end 119862119881is the
effective viscous damping coefficient 120574 = 1 if the downstreamend is supported so the displacement is zero and 120574 = 0 if it is
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 3
Table 1 Natural frequency of the fuel rod
Pellet material First order Second order Third order Fourth orderUranium dioxide 381436Hz 381579Hz 111947Hz 111966HzLead 37738Hz 37752Hz 11076Hz 11078Hz
y
zU
l
c1 c2
k2k1
Figure 3 Schematic diagram of the fuel rod in axial flow
unsupported or elastically supported 119862119879is equal to 119862
119873and
defined as
119862
119873= 119862
119879=
4119862
119891
120587119862
119898
(2)
where 119862119891is the drag coefficient due to shear forces and 119862
119898is
added mass coefficientThe appropriate boundary conditions associated with the
equation of motion are as followsFor 119911 = 0
119896
1119906 + 119864119868
120597
3
119906
120597119911
3
= 0 119888
1
120597119906
120597119911
minus 119864119868
120597
2
119906
120597119911
2
= 0(3)
and for 119911 = 119897
119896
2119906 minus 119864119868
120597
3
119906
120597119911
3
= 0 119888
2
120597119906
120597119911
+ 119864119868
120597
2
119906
120597119911
2
= 0(4)
where 1198961and 1198962are displacement spring constants and 119888
1and
119888
2are torsional spring constants (see Figure 3)Unfortunately (1) associated with boundary conditions
(3) and (4) can only be used for the studies about linearvibration of the fuel rod Since the boundary conditionwith leakage flow is nonlinear and complex (3) and (4) areinappropriate as the boundary conditions for the calculationabout leakage-flow-induced vibration of the fuel rod On theother hand since the boundary conditions are not taken intoaccount during (1) derivation process (1) is still applicablefor calculation of leakage-flow-induced vibration Thereforeonly a series of appropriate boundary conditions are neededfor (1) to accurately calculate the vibration behavior of fuelrod caused by leakage flow and the experimental result in thispaper could provide a benchmark to validate the availabilityof boundary conditions
3 Details of Experiment
31 Experimental Setup The experimental facility is shownin Figure 4 The flow-induced vibration test section consistsof two parts (1) a visualized channel made of acrylic with
Pressuregauge
Flow meter
Flow meterPump
Water tank
Dirt separator
Valve
Valve Valve
Testsection
Figure 4 Schematic diagram of experimental loop
Table 2 Experimental conditions and geometry parameters of thetest section
Temperature of water 25∘COperational pressure 01MpaSize of channel 20mm times 20mm times 725mmDiameter of fuel rod 8mmLength of fuel rod 710mm
water flowing axially through it and (2) a small scale fuelassembly The fuel assembly in the experiment has the samegeometry parameters as that in supercritical water loop Thecladding is made of stainless steel 316L which is the same asthe material used in supercritical water loop The material ofpellet in the experiment is lead whose density (113 gcm3)is similar to the density of uranium dioxide (1096 gcm3)In order to demonstrate the rationality of using lead as areplacement for uranium dioxide the modal analysis wasmade for the fuel rod From the results ofmodal analysis listedin Table 1 it is easy to see there is little difference betweenthe natural frequencies of fuel rods with two kinds of pelletsmade of uranium dioxide and lead respectively Since thevibration behavior of fuel rods is strongly dependent on theirnatural frequencies it is proper to use lead as a replacementfor uranium dioxide
The bottom ends of the rods are fully constrained Mean-while there is a 02mm clearance between the top end ofthe rod and the locating hole The displacements at midpointof fuel rod are detected by a laser displacement sensor Thegeometry parameters of the test section and experimentalconditions are listed in Table 2 In addition the assemblydrawing and photo of the test section are shown in Figure 5
In order to investigate the effects of leakage flow on thecharacteristics of flow-induced vibration the effect of twodifferent spacers which is used to constrain the top end ofthe rod is researched respectively Figure 6(a) illustrates the
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
4 Science and Technology of Nuclear Installations
A-A
B-B
A-A
B-B
Local view
Displacementsensor
45mm
45mm
710
mm
02mm
Figure 5The collocation and geometry of the fuel assembly and testsection
Hole Clearance
Fuel rod
(a)
Spacer
(b)
Figure 6 Schematic diagram of two types of spacers
top end of fuel rod is constrained by the spacer with throughholes meaning there is a leakage flow across the clearanceThis case is called ldquothrough hole caserdquo In Figure 6(b) sincethe top end of fuel rod is constrained by the spacer with blindholes there is no occurrence of leakage flowThis case is calledldquoblind hole caserdquo
32 Measuring Instrument Calibration For the small size ofchannel the contact measurement would have a significantinfluence on the flow field in the channel Thus the laserdisplacement sensor is used in the experiment to performthe noncontactmeasuringwithout influence on the flowfieldIt employs triangulation measurement principles whereby it
projects a beam of visible laser light that creates a spot on atarget surface Reflected light from the surface is viewed froman angle by a digital camera inside the sensor and the targetrsquosdisplacement is computed from the image pixel data
However in the process ofmeasuring the vibration of fuelrod fixed in a channel with room-temperature water flowinginside the refraction caused by acrylic water and air wouldlead to themeasurement deviation For accurately measuringthe vibration of the fuel rods it is necessary to correctthe deviation of measurement caused by refraction beforecarrying out the flow-induced vibration (FIV) experiment
Generally the measuring instrument calibration can beperformed by refraction theoretical analysis for laser dis-placement sensorHowever since the channel in practice can-not bemade evenly by the acrylicmaterial the nonuniformityof channel could lead to the refraction occurring not only onthe surface but also inside the channel and this phenomenonis difficult to predict in theory Thus a device is employed tocorrect the measurement deviation caused by refraction It iscomposed of a micrometer and a container made of acrylicas Figure 7 shows
The thickness of the container 119889
1is the same as the
thickness of channel 11988910158401
in FIV experiment meanwhilethe distance from the micrometer to the inner face of thecontainer 119889
2is equal to that from fuel rod to the inner wall
of the channel 11988910158402
Therefore the measured deviation causedby refraction is the same when the sensor is used to measurethe movements of the fuel rods and micrometer respectivelyWhen the top end of micrometer moves forward to a littledistance Δ119909 a corresponding measured value Δ119910 can beobtained by the laser displacement sensor The differencebetweenΔ119909 andΔ119910 is themeasured deviation caused by laserrefraction Several movements would be made to get two setsof data Δ119909
119899(119899 = 1 2 3 4 ) and Δ119910
119899(119899 = 1 2 3 4 )
The calibration curve for laser displacement sensor couldbe obtained by a linear fitting with the two sets of data asFigure 8 shows The equation of the curve is written as
119910 = 072582119909 minus 1790196 (5)
where 119909 is the actual position of the micrometer and 119910 is themeasured position
Assuming the actual position is 1199091 themeasured position
is 1199101 then (5) becomes
119910
1= 072582119909
1minus 1790196 (6)
Moreover if the actual position is 1199092and the measured
position is 1199102 (5) becomes
119910
2= 072582119909
2minus 1790196 (7)
Subtracting (7) to (6) gives
119910
2minus 119910
1= 072582 (119909
2minus 119909
1) (8)
Noting (1199092minus119909
1) is the actual displacement of micrometer
Δ119909 and (1199102minus119910
1) is the correspondingmeasured displacement
Δ119910 so (8) becomes
Δ119910 = 072582 sdot Δ119909 (9)
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 5
Micrometer
Water
Container
Sensor
Channel wall
Fuel rod
d2
d1
d998400
2
d998400
1
Δxn(n = 1 2 3 )
Δyn(n = 1 2 3 )
Figure 7 Measurement calibration device
350
300
250
200
150
100
50
0
300 350 400 450250200150100500
Mea
sure
d po
sitio
n by
sens
or (120583
m)
Actual position of micrometer (120583m)
Experimental valueLinear fit curve
Figure 8 Measurement calibration curve
From (9) it is clear that when the micrometer movesforward 1 120583m the correspondingmeasured value by displace-ment sensor is 072582 120583m with a deviation of 027418120583mwhich is caused by the refraction For eliminating the devi-ation it is necessary to correct the measured value of laserdisplacement sensor according to (9)
33 Structure Improvement Generally the vibration behav-ior of fuel rods is random in FIV experiment includingforward motion and lateral motion Since the fuel rods arecentrosymmetric structure statistical characteristics of thevibration in forward direction and lateral direction are thesame Thus it is only needed to measure the forward motionduring the experiment to know the vibration characteristicof fuel rods However when a fuel rod vibrates in bothdirections as shown in Figure 9(a) the position of the laserspot projected by the sensor will change with the vibrationof fuel rod moving along the surface of cylindrical rod andcausing the measured value 119889
1to be larger than the actual
displacement 1198892 That has a substantial influence on the
result In order to solve this problem the structure of fuel rodhas been improved by fixing a tiny metal sheet on the surfaceof fuel rod The size of metal sheet is shown in Figure 9(c)and one side of the sheet is flat In this way even thoughthe position of laser spot still changes with the movement of
fuel rod the laser spot could move on a flat surface insteadof curved surface as shown in Figure 9(b) As a result inthis situation the measured value 1198891015840
1
is the same as the actualdisplacement 1198891015840
2
34 Measuring System The hardware of the measuring sys-tem mainly consists of a noncontact and high-speed laserdisplacement sensor (LTC-025-04-SA MTI) a high-speeddata acquisition card (Daq3000 Iotech) and data acquisitionsoft system (DASYLab National Instruments) The measur-ing system is shown in Figure 10 In order to reduce thesampling signal bias and frequency alias a low-pass filter isused to process the detected signal for preventing the high-frequency signal In addition a correction module is addedto correct the measurement deviation caused by refractionaccording to (9)
4 The Experimental Results and Analysis
41 Reliability Analysis In practice for reducing the difficultyof FIV experiment the experiment is always carried outat the low temperature and pressure conditions such asFIV experiment of heat exchange tube in steam generatorIn the same way the FIV experiment of small scale fuelassembly in supercritical water loop is also carried out atthe low temperature and pressure conditions Even thoughthe natural frequencies of fuel rods in FIV experiment arealmost the same with those in the supercritical water loopthe vibration behaviors are different because of the differencebetween the supercritical fluid and subcritical fluid in twocases Thus a reliability analysis is needed to make sure theexperimental result is reliable Because the bottom ends ofrods are fully constrained the fuel rods have no displacementin the axial direction even if there is a density gradient alongthe rod induced by heating Therefore it is only needed toanalyze the difference of radial displacement in two cases
Actually the average value of fluid exciting force 119865 whichcould cause radial displacement of fuel rod is proportionalto the density of fluid 120588 and the square of velocity 119881 (10)Moreover when the size of channel is fixed 119865 is proportionalto the square of flow rate 119876 (11) Consider
119865 prop 120588 sdot 119881
2 (10)
119865 prop 120588 sdot (
119876
119904
)
2
(11)
Since the fluid used in the experiment is normal tem-perature water (25∘C) whose density is larger than that of
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
6 Science and Technology of Nuclear Installations
Position 1
Position 2
X
Y
d2d1
SensorO
(a) Original structure 1198891gt 1198892
d998400
2d998400
1
Sensor
(b) Improved structure 11988910158401
=
119889
1015840
2
3m
m
3mm
05
mm
(c) Size of metal sheet
Figure 9 Schematic of improved structure
Displacement of the
Displacement
Correctionmodule
sensor
Final displacementsignals signals signals
Digital signalsComputer
Initial displacement Initial voltage
Analog signalsinstrument
Data acquisition
Filter module
Arithmetic module
fuel rod
(below 30Hz)
Figure 10 Schematic diagram of data acquisition system
supercritical water according to (10) it can be noted thatthe average value of fluid exciting force
119865 in the experimentis larger than that in the supercritical water loop under thesame flow rate In consequence the average value of axialdisplacement in the experiment is much larger meaning theexperimental results are conservative Therefore if the fuelrod can meet the mechanical performance requirements inthe FIV experiment it can definitely meet the requirementsof safety and reliability in the supercritical water loop
42 DataValidation For the vibration induced by turbulenceand leakage flow which is random [3] an infinite recordshould theoretically be used to describe this process How-ever only a finite length record and data can be obtained inthe experiment So as to use the characteristics of a finitelength time history to characterize the whole process ofrandom vibration this vibration has to be ergodic [10] Sobefore making further analysis of the experimental data itis necessary to make sure whether the random vibrationof fuel rod is ergodic or not Therefore the experimenthas been repeated several times under the same conditionsand the comparison among the statistical values of theseexperimental results is made Table 3 shows the root meansquare (rms) displacement of the fuel rod in through holecase It can easily be found from Table 3 that the rmsdisplacement is almost the same in these experiments underthe condition of the same flow rate That means the vibrationof fuel rod is a stationary ergodic process
43 Spectral Analysis Since there is no Fourier transformfor a random signal its spectral characteristics are alwayscharacterized by the power spectral density (PSD) which isthe measurement for the distribution of vibrational energyin frequency domain and contains the information aboutamplitude of vibration in time domain [11] Figures 11 and12 separately show the displacement PSD of the fuel rod intwo different cases with different flow rate It is shown inFigure 11 that with the increase in flow rate there are obviouschanges in power spectrum curves at the frequency range of6ndash20Hz According to themeaning of PSDmentioned aboveit is certain that with the increase of flow rate the proportionof vibrational energy distribution and the amplitude ofvibration increase at the frequency range of 6ndash20Hz Incomparison it can be easily concluded from Figure 12 thatthere is no significant change in power spectrum curveunder the same conditions except that the magnitude ofspectrum tends to become larger The reason for that is thatthe increase of flow velocity will lead to the enhancement ofturbulent-boundary-layer pressure fluctuations which is themost important near-field noise to induce the vibration of fuelrods [12]
As shown in Figure 13 both the shape of curves and themagnitude of spectrums in two cases are essentially the samein low-frequency bands below 5Hz at 119902V = 362m3h butthe trends of two curves become much different after 5HzThe curve declines gradually with frequency in blind holecase On the contrary in the through hole case the curveshows an ascending trend in the frequency ranging from
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 7
Table 3 Root mean square displacement of the fuel rod in through hole case
Flow rate (m3h)Root mean square displacement (120583m)
1st 2nd 3th Average value063 1071 1133 1108 1104139 1317 1362 1374 1351212 1508 1497 1534 1513288 1704 1722 1686 1703362 1969 1913 1942 1941
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 11 Displacement power spectral density of the fuel rod inthrough hole case
6Hz to 13Hz and reaches the peak value at 13Hz and thenthe curve decreases after 13Hz As a consequence it can beconcluded that the differences in PSD between these twocases are mainly caused by leakage flow occurring on thetop of fuel rods Furthermore the influence of leakage flowincludes two aspects one is the change in the distribution ofvibrational energy in spectrum and the other is the increasein the magnitude of spectrum at the frequency range of6ndash20Hz
Theoretically since (1) is applicable for the studies ofleakage-flow-induced vibration of the fuel rod it can beused to calculate the vibration of fuel rod caused by leakageflow only if associated with appropriate boundary conditionsOn the other hand if the boundary conditions are not setproperly the computational result of (1) could not show theinfluence of leakage flow mentioned above Therefore theexperimental results provide a benchmark for the theoreticalcalculation and comparing the experimental result andnumerical result could determine whether the boundarycondition is proper for the studies related to leakage-flow-induced vibration
It is shown in Figure 14 that the power spectrum curvesin two cases essentially have the same changing tendency
0 5 10 15 20 25Frequency (Hz)
30 35
minus120
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
q = 362m3hq = 288m3hq = 139m3h
Figure 12 Displacement power spectral density of the fuel rod inblind hole case
0 5 10 15 20 25Frequency (Hz)
30 35 40
minus120
minus125
minus130
minus135
minus140
Pow
er sp
ectr
a (dB
)
Through hole caseBlind hole case
Figure 13 Displacement power spectral density of the fuel rod intwo cases at 119902V = 362m3h
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
8 Science and Technology of Nuclear Installations
0 5 10 15 20 25Frequency (Hz)
Through hole caseBlind hole case
30 35minus150
minus125
minus130
minus135
minus140
minus145
Pow
er sp
ectr
a (dB
)
Figure 14 Displacement power spectral density of the fuel rod intwo cases at 119902V = 062m3h
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 15 Probability density distributions of displacements inthrough hole case at 119902V = 362m3h
at 119902V = 062m3h and the reason is that the influence ofleakage flow weakens as the flow rate decreases Comparedwith turbulent-boundary-layer pressure fluctuations leakageflow has little influence on the vibration of fuel rods when theflow rate reduces to a certain value
44 Statistical Analysis After making a statistical analysison the vibration behavior of fuel rods at 119902V = 362m3hthe probability density distributions of displacements atmidpoint in both cases are obtained they all could be fittedwell by a normal distribution function (see Figures 15 and 16)From the comparison it can be found that the distribution ofvibration displacements in blind hole case in contrast to theone in through hole case is more concentrated at 0 120583m On
0030
0025
0020
0015
0010
0005
0000
Prob
abili
ty d
ensit
y fu
nctio
np(x)
minus100 100minus75 75minus50 50minus25 0 25
Statistic of experimental dataNormal distribution curve
Displacement x (120583m)
Figure 16 Probability density distributions of displacements inblind hole case at 119902V = 362m3h
Through hole caseBlind hole case
20
18
16
14
12
1010 15 20 25 30 35 40
Flow rate (m3h)
Rms d
ispla
cem
ent (120583
m)
05
Figure 17 Root-mean-square displacement changing with flow ratein two cases
the basis of probability statistics theory it can be determinedthat the variance of random vibration which represents thedynamic component of vibration amplitude is smaller inblind hole case than that in through hole case The reason isthe existence of leakage flow in through hole case as well
45 Analysis of the Root Mean Square Displacement Theabsolute value of amplitude at certain time is meaninglessbecause the vibration of fuel rod is random Therefore wecalculate the root mean square (rms) displacement whichis a statistical measurement of the magnitude of the varyingdisplacement and contains the information about vibrationenergy The rms displacements at midpoint changing withflow rate in two cases are compared in Figure 17 It is found
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970
Science and Technology of Nuclear Installations 9
Left Right
Spacer
Fuel rod
V
Figure 18 Diagram to explain the mechanism associated withleakage-flow-induced instability
that the uptrend of rms displacement in through hole case ismore obvious than that in blind hole case In through holecase if the rod has a small rightward velocity 119881 caused byturbulence it will lead to the reduction of right side clearance(see Figure 18) As a result the flow across the right sideclearance will decrease with time The opposite situationexists with respect to the flow in the left side clearanceBecause of flow velocity redistribution in the clearance thereare changes in the static pressure on both sides of clearanceconsequently It gives rise to a net fluid force acting on thetop end of fuel rod in the same direction as the motionHence this results in amplified motion Under the sameother conditions the difference between rms displacementsin two different cases is strongly dependent on leakage flowTherefore in order to reduce the flow-induced vibrationwhich may lead to fatigue of the fuel rods it is morereasonable to use the spacers with blind hole to assemble thesmall scale fuel rods in the supercritical water loop
5 Conclusions
An experiment is made to investigate flow-induced vibrationof rods exposed to an axial flowwithin a rigid square channelespecially the vibration caused by leakage flow In order toimprove the experimental accuracymeasurement calibrationis performed to correct the measurement deviation causedby refraction before the FIV experiment According to theexperimental data and analytical results three useful conclu-sions are obtained as follows
(1) When flow rate is low the vibration of rods is mainlycaused by turbulence flow and leakage flow has littleinfluence on that
(2) As flow rate increases the influence of leakage flowbecomes obvious which could change the distribu-tion of vibrational energy in spectrum increasingthe vibrational energy in high-frequency band Fur-thermore it could be treated as a benchmark forthe theoretical studies to validate the applicability of
boundary condition set for leakage flow If a boundarycondition is set properly the result of theoreticalcalculation would show the influence of leakage flowfound in the experiment otherwise this boundarycondition is not set properly
(3) Under the same other conditions the differencebetween rms displacements in two different cases isstrongly dependent on leakage flow Therefore fromthe point of view of structure safety and reliability itis more reasonable to improve the design by using thespacerswith blindhole to assemble the small scale fuelrods in the supercritical water loop
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R D Blevins Flow-Induced Vibration Van Nostrand ReinholdCompany 1977
[2] D E Hobson ldquoFluid-elastic instabilities caused by flow inan annulusrdquo in Proceedings of 3rd International Conference onVibration in Nuclear Plant pp 421ndash428 Keswick UK 1982
[3] S S Chen Flow-Induced Vibration of Circular CylindricalStructures Springer Berlin Germany 1987
[4] M P Paıdoussis ldquoA review of flow-induced vibrations inreactors and reactor componentsrdquo Journal Nuclear Engineeringand Design vol 74 no 1 pp 31ndash60 1983
[5] D Mateescu and M P Paidoussis ldquoUnsteady potential flow inan axially variable annulus and its effect on the dynamics ofthe oscillating rigid center-bodyrdquo Journal of Fluids EngineeringTransactions of the ASME vol 107 no 3 pp 421ndash427 1985
[6] M Arai and K Tajima ldquoLeakage-flow-induced vibrations of anaxisymmetric body part 1mdashanalysis of themoment acting on anaxisymmetric body for rotational motionrdquo JSME InternationalJournal C vol 41 no 3 pp 347ndash354 1998
[7] D-W Li S Kaneko and S Hayama ldquoA study on annularleakage-flow-induced vibrationsrdquo Journal of Fluids and Struc-tures vol 16 no 7 pp 909ndash930 2002
[8] M A Langthjem H Morita T Nakamura and M NakanoldquoA flexible rod in annular leakage flow influence of turbulenceand equilibrium offset and analysis of instability mechanismsrdquoJournal of Fluids and Structures vol 22 no 5 pp 617ndash645 2006
[9] K Fujita H Morikazu and A Shintani ldquoA considerationon pre- and post-instability of an axisymmetric elastic beamsubjected to axial leakage flowrdquo Journal of Fluids and Structuresvol 23 no 3 pp 463ndash478 2007
[10] D E Newland An Introduction to Random Vibrations andSpectral Analysis China Machine Press Beijing China 1984
[11] Z Q Hu Q Y Fa et al Technique of Random Vibration TestChinese Metrology Press Beijing China 1984
[12] S S Chen ldquoResponse of a flexible rod to near-field flow raterdquoin Proceedings of the Conference on Flow-Induced Vibrations inReactor System Components (ANL-7685 rsquo70) pp 5ndash31 ArgonneNational Laboratory Argonne Ill USA 1970