Heat Transfer Correlations in Nuclear Reactor Safety Calculations

Mord JUNE 1985

Heat Transfer Correlations in Nuclear Reactor Safety Calculations

SURFACE HEAT FLUX

Nordic liaison committee for atomic energy

Nordisk Nordiskakontaktorgan for kontaktorganet foratomenergispørgsmål atomenergifrågor

Pohjoismainen Nordicatomienergia- liaison committee foryhdyselin atomic energy

RISØ-M-2504

HEAT TRANSFER CORRELATIONS INNUCLEAR REACTOR SAFETY CALCULATIONS

SAK-5

H. Abel-Larsen, RisøA. Olsen,J. Miettinen,T. Siikonen,J. Rasmussen,A. Sjoberg,K. Becker,

RisøVTTVTT

IFE

StudsvikKTH

June 1985

Risø: Risø National Laboratory, DenmarkVTT: Technical Research Centre of FinlandIFE: Institute for Energy Technology, NorwayStudsvik: Studsvik Energiteknik AB, SwedenKTH: Royal Institute of Technology, Stockholm, Sweden

ISBN 87-550-1109-8ISSN 0418-6435minab/gotab Stockholm 1985

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ABSTRACT

Heat transfer correlations, most of them incorporated in theheat transfer packages of the nuclear reactor safety computerprogrammes RELAP-5, TRAC (PF1) and NORA have been testedagainst a relevant set of transient and steady-state ex-periments. In addition to usually measured parameters the cal-culations provided information on other physical parameters.Results åre presented and discussed.

The report consists of a main report (Vol.I) and appendices(Vol.II). Chapters 3,4 and 5 of the main report åre primarilyintended for computer programme users. Chapter 6 is recommendedfor those looking for main results rather than details. Theappendices will be useful for computer programme developers.

INIS descriptors;

CRITICAL HEAT FLUX - COMPARATIVE EVALUATIONS - CORRELATIONS -COORDINATED RESEARCH PROGRAMS - DENMARK - DROPLETS - EVAPOR-ATION - FINLAND - FAILURES - PUEL ELEMENTS - FILM BOILING-FORCED CONVECTION - HEAT TRANSFER - LOSS OF COOLANT - NORWAY -N CODES - NUCLEATE BOILING - NATURAL CONVECTION - R CODES -

REACTOR SAFETY - SWEDEN - T CODES - TRANSIENT - TRANSITIONBOILING - THERMAL RADIATION

This report is part of the safety programme sponsored byNKA, the Nordic Liaison Committee for Atomic Energy, 1981-85.The project work has been partly financed by the NordicCouncil of Ministers.

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LIST OF CONTENTS

VOLUME l: Page

ABSTRACT .............................................. 1SUMMARY ............................................... 9SAMMENFATNING (Danish summary)......................... 13

1. INTRODUCTION ....................................... 17

1.1. The aim of the project ........................ 171.2. Organisation of the report .................... 171.3. Heat transfer regions ......................... 18

2. ORGANIZATION OF THE PROJECT ........................ 252.1. Participating organizations ................... 252.2. Distribution of work .......................... 26

3. PRESENT KNOWLEDGE .................................. 273.1. General considerations ........................ 273.2. Heat transfer in different flow regions ....... 28

4. COMPARISON OF CORRELATIONS WITH DATA ............... 344.1. Computer programmes used ...................... 344.2. Comparisons with data ......................... 354.3. Experiences using the computer programmes ..... 384.4. Comparisons using separate programmes ......... 39

5. DISCUSSIONS AND RECOMMENDATIONS .................... 415.1. Nucleate and forced convective boiling ........ 415.2. Critical heat flux ............................ 425.3. Transition boiling ............................ 435.4. Rewetting ..................................... 445.5. Film boiling .................................. 455.6. Interfacial heat transfer ..................... 48

6. CONCLUSION.......................................... 52

NOMENCLATURE .......................................... 55

REFERENCES ............................................ 58

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VOLUME II : Page

APPENDIX A. PRESENT KNOWLEDGE ......................... 8

A1. Nucleate boiling and forced convective boiling 8A2. Critical heat flux ........................... 11A3. Transition boiling ........................... 15A4. Rewetting .................................... 25A5. Film boiling ................................. 31A6. Interfacial heat transfer .................... 45

APPENDIX B. COMPARISON WITH DATA ...................... 52

B1 . Heat transfer package ........................ 52B1.1. RELAP-5 ...................................... 52

B1.2. TRAC(PF1) .................................... 54B1.3. NORA ......................................... 60B2. Comparison with data ......................... 61B3. Experiences using computer programmes ........ 100B4. Comparison using separate programmes ......... 103B4.1. Critical heat flux ........................... 103B4.2. Transition boiling ........................... 109

APPENDIX C. DISPERSED FLOW ............................ 129

C1. Droplet generation ........................... 129C2. Droplet flow ................................. 136C3. Droplet flow heat transfer.................... 153

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PIGURES. Page

VOLUME I:

1. Boiling curve ................................ 19

2. Heat transfer regions ........................ 21

3. Heat transfer regions (Tw<TcHp) .............. 22

4. Heat transfer regions (TW>TCHF) •••••••••••••• 23

5. Heat transfer modes in two-phase flow ........ 30

6. Critical heat flux mechanisms ................ 33

VOLUME II:

A3.1. Droplet deposition ........................... 22

A5.1. Flow transitions at CHF ...................... 41

A5.2. Types of inverted annular film ............... 42

A5.3. Comparison between measured and calculated ...results - heat transfer coefficient Bromley .. 43

A5.4. As above but modified Bromley ................ 44

A6.1. Pressure vs. time. Comparison between measuredand calculated results........................ 50

A6.2. Critical mass flux vs. pressure .............. 51

A6.3. Critical mass flux vs. pipe length ........... 51

B1.1. Heat transfer coefficient surface using heattransfer package of RELAP-5 with default CHF-correlation ................................. 55

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B1.2. As B1.1 but Beckers CHF-correlation and voidlimit excluded ............................... 56

B2.1. Roumy case 1 ................................ 63

B2.2. Roumy case 2 ................................ 64

B2.3. Mass flow vs. time .......................... 65

B2.4. CHF and heat rate vs. time .................. 65

B2.5. Outlet wall temperature vs. time ............ 66

B2.6. Mass flow vs. time .......................... 66

B2.7. CHF and heat rate vs. time .................. 67

B2.8. Outlet wall temperature vs. time ............ 67

B2.9. CE/EPRI single tube blowdown loop ........... 70

B2.10. Void vs. time ............................... 71

B2.11. Temperature vs. time ........................ 71

B2.12. Temperature vs. time ........................ 72

B2.13. Pressure vs. time ........................... 72

B2.14. Mass flux vs. time .......................... 73

B2.15. Power vs. time .............................. 73

B2.16. Outlet node void vs. time ................... 74

B2.17. Outlet temperature vs. time ................. 74

B2.18. Wall temperature vs. time ................... 75

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B2.19. Wall temperature vs. time .................... 75

B2.20. Becker test section .......................... 80

B2.21. Temperature vs. length (NORA-case 1) ......... 81

B2.22. Temperature vs. length (RELAP-5 case 1) ...... 82

B2.23. Temperature vs. length (case 2) .............. 83




B2.27. Temperature vs. length (case 1 - new model)... 87




B2.31. ORNL-64 rod test bundle ...................... 92

B2.32. Grid and thermocouples, axial location ....... 93

B2.33. Temperature vs. length (case B) .............. 94

B2.34. Temperature vs. length (case C) .............. 95

B2.35. Temperature vs. length (case H) .............. 96

B2.36. Temperature vs. length (case K) .............. 97

B2.37. Temperature vs. length (case N) .............. 98

B2.38. Temperature vs. length (case O) .............. 99

B3.1. Velocity profiles in Becker case 1 ........... 104

B3.2. Calculated temperatures and vapour generationrate Becker case 1 ........................... 104

B3.3. Interfacial friction coefficient vs. void ... 105

B4.1.1. Local conditions hypothesis ................. 111

B4.1.2. Comparison between measured and predicted ...burnout power ............................... 112

B4.1.3. As above .................................... 113

B4.1.4. As above .................................... 114

B4.1.5. As above .................................... 115

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B4 .1 . 6 . Comparison between measured and predicted ...dryout heat flux - OF 64 .................... 116

B4 . 2 . 1 . Chen parameter B(P) vs. pressure ............ 120

B4.2.2. Exponent in decay factor vs. wall superheat . 121

B4.2.3. Comparison-measured-predicted-transitionboiling heat transfer coefficient ........... 124

B4.2.4. As above .................................... 125

B4.2.5. As above .................................... 126

B4.2.6. As above .................................... 127

B4.2.7. As above .................................... 128

C1.1. Droplet generation by entrainment ........... 130

C2.1. Distribution coefficient for velocity andvoid ........................................ 152

TABLES

VOL.I:

4.2.1. Selected test cases ........................... 37

VOL. II:

A1.I. Pre-CHF two-phase heat transfer correlation.... 9

Al.II. As above ...................................... 10

A2.I. CHF correlation tested by Leung ............... 14

A2.II. Testing of CHF correlation .................... 15

A3.I. Transition boiling heat transfer correlation .. 17-21

B4.1.I. RMS-errors obtained with the local hypothesis.. 110

— fl —

Steering committee for the NKA/SAK reactor safety programme,SAK-5 1981 - 1985:

C. Graslund(Chairman)

Swedish Nuclear Power Inspectorate, SKIStockholm

T. Eurola Finish Centre for Radiationand Nuclear Safety,Helsingfors

E. Hellstrand Studsvik Energiteknik AB,Nykoping, Sweden

D. Malnes Institute for Energy Technology,Norway

F. Marcus NKA,

Roskilde, Denmark

B. Micheelsen Risø National Laboratory,Roskilde, Denmark

E. Sokolowski Nuclear Safety Board ofthe Swedish Utilities,Sverige

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SUMMARY

Knowledge about temperatures on the surface of nuclear fuelrods plays an important role in nuclear reactor safety analysis.There is a need to calculate surface temperatures during opera-tional transients and postulated accidents under the assumptionthat the engineered safety features of the reactor åre activatedand working. A typical sequence to be calculated is a loss-of-coolant accident (LOCA).

The purpose of the calculatlons is to examine whether the in-tegrity of the fuel rod cladding, the first of three engi-neered barriers against radiological release, may be threatenedby the rise in surface temperature that may occur.

The integrity of the cladding depends on several individualphenomena, primarily metallurgical, all very sensitive to thecladding temperature.

For this purpose thermo-hydraulic computer programmes have beendeveloped e.g. the Arnerican programmes TRAC and RELAP-5 and theNorwegian programme NORA, all used in the present project.

In order to calculate realistic temperature differences betweenthe cladding surface and the coolant, reliable heat transfercorrelations åre needed for the different heat transfer regionsoccuring during a transient (cf. the front page figure).

The heat transfer correlations actually used in the computerprogrammes åre empirical to a high degree. They have beenfound from the results of independent steady-state experiments,using boundary conditions, that coincide with boundary condi-tions in safety calculations only partly.

A comprehensive test program is therefore necessary to showwhether the computer programmes can provide reasonable simu-lations of well-defined experiments that åre selected so thattheir conditions may be comparable with those occurring in thefuel element channels of a nuclear reactor.

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During the project, 16 experiments, (3 of them transient and 13steady state) were chosen, and their results were compared withcalculations with the computer programmes TRAC (PF1), RELAP-5and NORA.

Not all relevant parameters for the evaluation of a correlationcan be measured in an experiment. Those missing will be calcu-lated by the computer programmes according to their inherentlogics and models.

Using the transient experiments it turned out that the heattransfer packages in the computer programmes did not give anadequate picture. This may be due to the influence of othertransport phenomena (subcooled void, slip, thermodynamic non-equilibrium) just as different empirical correlations apartfrom the heat transfer correlations may dominate the calculation.More simplified experiments appeared to be needed, preferablysteady state experiments with well-defined boundary conditions.These experiments would need to cover the complete Spectrum ofheat transfer modes in each flow region with the critical heatflux (CHF) exceeded. CHF is characterized by the loss ofcontact between the liquid coolant and the cladding surface,when the heat flux applied to the surface is monotonouslyincreased to this point.

CHF is an important parameter, since, with an appropriatesafety margin, it separates normal and abnormal operation ofa nuclear reactor.

The heat transfer correlations used in pre-CHF flow regionswere found to be adequate. The heat transfer in these regionsis very efficient and will not be a limiting factor for thefuel and cladding during an operational transient or a postu-lated loss of coolant accident.

The CHF correlations used in the computer programmes (Biasi,CISE-4) åre, however, not adequate. The correlations cannotpredict the locus of CHF with sufficient accuracy.

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As a consequence, it was decided to start an independent exam-ination of four relevant CHF correlations: Barnett, Becker,Biasi and CISE-4, using results from six full-scale rod bundleexperiments (table B4.1.I), and using a separately developedcomputer programme.

The conclusion from these calculations is that the Biasi andCISE-4 correlations cannot predict the CHF-conditions withadequate accuracy. An explanation may be that these two corre-lations åre developed from single tube data and have no pro-visions to incorporate the influence of unheated surfaces andinternal rod-to-rod power distribution.

The two other correlations, developed in the late 1960's forrod bundle geometries, correlate the experimental data better.

The post-CHF heat transfer conditions strongly depend on thelocus of CHF. As the locus could not be calculated with suffi-cient accuracy it was fixed in the calculations as measuredin the continuous examinations of the 13 steady state experi-ments.

After this the surface temperatures were recalculated. Theywere too low in RELAP-5 and TRAC, too high in NORA. These devi-ations were referred back to erroneous predictions of thethermodynamic nonequilibrium.

The thermodynamic nonequilibrium is governed primarily by masstransfer between droplets and vapour due to interfacial heattransfer. A decrease in the vapour generation rate will in-crease the vapour temperature (superheating) under equal condi-tions thus allowing the thermodynamic nonequilibrium to be morepronounced. Based on this it must be concluded that the inter-facial heat transfer coefficients åre too high in RELAP-5 andTRAC too low in NORA.

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A recently developed semi-empirical vapour generation modelwas therefore implemented in the programmes. Hereafter, theresults were substantially improved, and a better agreement wasobtained between measured and calculated post-CHF surface temp-eratures.

It is obvious even from these last few calculations, togetherwith the examinations of transition boiling heat transfer usinga separately developed programme, that more realistic and phe-nomenological heat transfer models have to be developed for thepost-CHF regions. It is recognized that the degree of thermo-dynamic nonequilibrium at any axial level will depend on theupstream competition between the heat transfer mechanisms wall-to-vapour by convection, wall-to-droplet by droplet impingmenton the surface and vapour-to-droplet by interfacial heat trans-fer.

The present project has been limited to application of the heatcorrelations in nuclear reactors. However, the same basictechnical questions concerning heat transfer in fluids withdroplets or particles and the correlations used to descibe theheat transfer find wide application in a number of fieldssuch as chemical processes, fluidized bed combustion, spraycooling, heat and mass transfer in evaporators, once-throughsteam generators to name a few.

The problems described in this report åre an example of howadvanced methods developed for the nuclear area can contributeto other technical areas of current interest.

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SAMMENFATNING

Uranbrændslet i en kernekraftreaktor er atxrkt radioaktivt.Det er vigtigt, at brændslet indesluttes effektivt, så ingenradioaktive stoffer kan frigøres til omgivelserne. Tre kon-struerede barrierer tjener dette formal. De tre barriererer først indkapslingen, der indealutter det nukleare brændsel,dernæst reaktortanken, der omslutter reaktorkernen og detprimære kølesystem og endelig den tryktætte reaktorbygning,der indslutter reaktoranlæggets primære systemer.

Et vigtigt led i sikkerhedsanalysen af kernekraftreakt or arer at eftervise, at temperaturerne på overfladen af indkaps-lingen under unormale driftsforstyrrelser og pastulerede u-held, som f.eks. tab-af'-kølemiddel-uheld, ikke overstigeren fastsat værdi, når reaktoranlæggets beskyttesessystemervirker.

Overstiger indkapslingslingstemperaturen den fastsatte grænse-værdi kan indkapslingen revne. Årsagen hertil er flere metal-lurgiske fænomener alle følsomme overfor temperaturen.

Den absolutte størrelse af temperaturen afhænger af dels,hvor godt man kan bestemme de metallurgiake fænomeners tem-peratur afhængighed og dels, hvor godt man kan bestemme ind-kapslingens overfladetemperatur.

Projektet har beskæftiget sig med een side af sidstnævntepunkt.

Beregning af realistiske temperaturforskelle mellem indkaps-lingens overflade og kølemidlet forudsætter pålidelige varme-overgangskorrelationer. Ved en korrelation skal her forståset matematisk udtryk, der nok støtter sig til fysiske prin-cipper, men primært er baseret på statistisk behandling afforsøgsdata.

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Det primære formål med nærværende projekt var at undersøgepålideligheden af nogle udvalgte korrelationer for varmetrane-porten med henblik på deres anvendelse i datamaskine-programmer,der modellerer forholdene i reaktorkernen under et uheldsforløb.

Et eksempel på en brxndelsstavs overfladetemperatur undet såvelnormal drift som under et uheldsforløb er givet på forsiden afdenne rapport. Kølemidlet er kogende vand, d.v.s. der er bådedamp og vand tilstede (to-fase køling).

Ved normal drift af en kernekraftreaktor skal overfladetempe-raturen af indkapslingen holdes under den temperatur, der svarertil den kritiske varmestrøm (punkt C på forsidefiguren).

Undersøgelsen af de korrelationer, som anvendes ved bestemmel-sen af varmetransporten før kritisk varmestrøm, bekræftede, atde er tilstrækkelig pålidelige. Varmetransporten her er megeteffektiv og vil ikke vxre en begrænsende faktor for indkaps-lingen .

Kritisk varmestrøm er karakteriseret ved tabet af kontakt mellemindkapslingens overflade og kølevand på grund af dannelsenaf et overhedet lag af damp.

De korrelationer, som blev benyttet til bestemmelse af vær-

dien af og stedet for kritisk varmestrøm i de anvendte data-maskine-programmer var ikke tilstrækkelig pålidelige. En uaf-hængig undersøgelse med et separat udviklet program blev derforudført på dels de to anvendte korrelationer og dels to andre,ældre korrelationer. Resultatet var, at de to xldre korrela-tioner bedre kunne forudsige forsøgsdata fra 6 forsøg medelektrisk opvarmede brændselselementer i f uld-skala.

Undersøgelsen af korrelationer for varmetransporten efter kri-tisk varmestrøm viser, at de tilstrækkelig pålideligt kaneftervise målte overfladetemperaturer i de forsøg, som erbenyttet ved sammenligningen, når der tages nødvendigt hensyntil to fysiske fænomener:

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1. termodynamisk uligevxgt2. dråbekøling.

Ved den termodynamiske uligevægt skal forstås, at damptempera-turen, efter at den kritiske varmestrøm er passeret, kan blivehøjere end vandtemperaturen, idet varmetransporten primært vilske til dampen og herfra videre til vanddråber i dampen. Dampenoverhedes d.v.s. varmetransporten til dråber er ikke i lige-vægt med varmetransporten til dampen. Ved at tage hensyn tildenne overhedning kunne en væsentlig bedre overensstemmelsemellem forsøgsdata og beregnede overfladetemperaturer opnas.

Resultaterne fra undersøgelsen af termodynamisk uligevxgt ogresultater fra undersøgelsen af den såkaldte transition-kogning(området mellem punkterne C og D på forsidefiguren) viser, atdrabekølingen er et særdeles vigtigt led i varmetransporten.

Ved transitionkogning er varmetransporten bedre end i områdetfor filmkogning (området mellem D og E på forsidefiguren),fordi dråber, som rammer indkapslingens overflade, kan vædeoverfladen. Kølingen forstærkes ved direkte fordampning afdråberne.

De to nævnte fænomener afhænger stærkt af hinanden, idet gradenaf den termodynamiske uligevxgt vil afhænge af konkurrenaen

mellem varmetransporten: indkapslingsoverflade til damp vedkonvektion, indkapslingsoverflade til dråber ved fordampningog endelig damp til dråber ved såkaldt interfase varmeovergang.

Undersøgelserne i SAK-S projektet har klarlagt dråbernes betyd-ning for varmetransporten i omraderne efter kritisk varmestrøm.Man har vist, at om man vil forbedre pålideligheden er detnødvendigt at inddrage de fysiske fænomener mere d.v.s., der børudvikles mere realistiske modeller, som i højere grad baseres

på de fysiske fænomener end korrelationerne er. Det skal dogbemærkes, at fænomenologiske modeller, der kan bestå af flerematematiske udtryk, kan øge kompleksiteten af beregningspro-grammet og beregningstiden. Et valg mellem den detaljerede fæno-menologiske model og den statistiske korrelation kan derfor blive

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nødvendig.

Undersøgelserne har været begrænset til varmetransport i kerne-kraf'treaktorer, men de grundlæggende fysiske og tekniske spørgs-mål er de samme for varmetransport indenfor store omrader afden moderne teknik, der saledes også kan drage nytte af under-søgelserne .

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1. INTRODUCTION

1.1. The aim of the project

The aim is to establish a set of reliable heat transfer corre-lations primarily for application in best-estimate computerprogrammes for nuclear reactor safety calculations.

Correlations in this sense åre sets of mathematical expressions,based on physical principles and experimental data, but restingprimarily on experimental data.

A best estimate is the most favourable with respect to reality.Favourable is in this context according to use and best know-ledge.

Reality refers to those transients that have to be evaluatedto assure the authorities that the safety of the system isacceptable. The transients åre all expected operational tran-sients and postulated accidents such as a break in the pressureboundary integrity resulting in a loss of core cooling water(Loss-of-Coolant-Accident, LOCA).

1.2. Organization of the report

This report contains a main report (VOL.I) and appendices (VOL.II)The main report covers the examined area from a more generalpoint of view. It provides a natural introduction to the appen-dices, which describe the work done in detail.

The participating organizations and the actual distribution ofthe work åre dealt with in Chapter 2.

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The project was initiated with a literature search. The generalconsiderations and results åre discussed in Chapter 3 andAppendix A.

The comparison of selected heat transfer correlations with ex-perimental data using the American computer programmes RELAP-5,TRAC(PF1), the Norwegian computer programme NORA, and separateprogrammes developed especially for this project is describedin Chapter 4 and Appendix B.

Discussions and recommendations based on the results attainedåre given in Chapter 5.

Chapter 6 contains the conclusion of the report.

1.3. Heat transfer regions

The heat transfer correlations åre closely connected with theactual flow region. The expressions flow region and heat trans-fer region may therefore be interchangeable.

The heat transfer regions and their occurrence in light waterreactors may be demonstrated by considering the temperaturecourse that a local spot on a heat transfer surface may experi-ence during a LOCA.

An example of such a temperature course as function of surfaceheat flux is shown in Fig. 1, the so-called boiling curve.The course from A to B represents the single-phase liquid flowregion. In the succeeding boiling region two different modesof flow can occur. In one mode, the nucleate boiling mode,the liquid is the continuous fluid; vapour is generated atspecific nucleation sites on the heating surface and vapourbubbles åre discretely distributed through the continuous,saturated liquid phase (liquid continuous). The other mode,the forced convective boiling mode, is characterized by thevapour as being the continuous fluid with the liquid distributedpartly as a film on the heating surface and partly as dropletsin the vapour (vapour continuous).

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- 20 -

When the heat flux applied to the sur face in contact with theliquid is progressively increased, a point is reached at whichthe continuous contact between the surface and the liquid islost and the critical heat flux (CHF) is attained.

The temperature course in Fig. 1 is shown for a heat flux-con-trolled surface, i.e. the heat flux is the independent variableas in electric and nuclear-heated systems.

When the surface heat flux in a heat flux-controlled systemis further increased the temperature will jump to point E. Thistemperature increase may cause a burnout in the real sense ofthe word and a certain safety margin to the CHF point has to besecured during normal operation of a nuclear reactor.

The surface temperature may go from F to E and further to D bydecreasing the heat flux. The temperature at D is the so-calledminimum film boiling temperature. From here the temperature mayjump to the nucleate boiling, i.e. a form of hysteresis effectmay exist.

During a strong transient, such as a LOCA, the fuel rods maybehave as a temperature-controlled system due to their thermalcapacities. The temperature course can then move into thetransition boiling flow region (from C to D), where the heattransfer is much better than in the film boiling flow region(from D to E and F).

The transition boiling flow region is active between the tempe-rature at CHF and the minimum film boiling temperature and canbe realized only in teraperature-controlled systems.

The flow regions as they may occur in emergency core cooling byreflood is shown in Fig. 2.

In general the logic in the selection of the heat transfer cor-lations may appear from these thoughts. Figures 3 and 4 showthe main features of the selection.

-21 -

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HEAT TRANSFER REGIONS

FIGURE 2

- 22

-


FIGURE 3

- 23 -


FIGURE 4.

- 24 -

From what is stated above, the heat transfer during the wholetemperature course can be traced to be dependent primarily onthe surface temperature and secondarily on whether the flow isliquid continuous or vapour continuous.

The transport equation of heat, first set up by Newton in 1701,is written:

Q = h'A-AT ,

where Q is the heat flow rate, A a characteristic surface area,AT a characteristic temperature difference, and the proportiona-lity factor h is defined as the heat transfer coefficient.

The heat transfer coefficient depends on the physical proper-ties of the fluid, mass flux, pressure, absolute vapour qualityand the geometry of the system.

- 25 -

2. ORGANIZATION OF THE PROJECT

The project is part of the safety programme of NKA, the NordicLiaison Committee for Atomic Energy and is in part financed byfunds from the Nordic Council of Ministers.

2.1. Participating organizations

The participants have been:

Risø National Laboratory, DenmarkH. Abel-LarsenA. Olsen (project leader),

Technical Research Centre of Finland, VTT,J. Miettinen,T. Si ikonen,

Institute for Energy Technology, IFE, Norway,J. Rasmussen,

Studsvik Energiteknik AB, Studsvik, Sweden,A. Sjoberg,

Royal Institute of Technology, KTH, Sweden,Department of Nuclear Energy,K.M. Becker.

- 26 -

2.2. Distribution of work

The logic classification of the boiling curve has been used asa base for the initial distribution of work in the literaturesearch.

IFE has examined the single phase liquid and the nucleate boil-ing and forced convective boiling flow region including thecritical heat flux.

Risø has examined the transition boiling flow region.

Studsvik examined the film boiling and single phase vapour flowregion.

VTT examined the quenching phenomena during the emergency corecooling through top-spray and bottom-reflooding and the inter-facial heat transfer.

Professor Becker has taken part in the proj eet since January1983 as a consultant.

- 27 -

3. PRESENT KNOWLEDGE

The result of a literature search is given in Appendix A. Belowis given a general view of the transport phenomena of heat forthe physical understanding of the heat transfer and its corre-lation.

3.1. General considerations

Some basic criteria and general requirements for the selectionof heat transfer correlation may be set up as follows (1):

a. The range of the experimental data base on whichthe correlation is based must coincide with therange of interest.

b. The deviation of the predicted results with the cor-relation from the experimental data should be low,i.e. a correlation with a lower standard deviationshould be selected over another correlation withhigher standard deviation.

c. If a. and b. åre satisfied, the correlation based onphenomenological or mechanistic considerations shouldbe preferred to the purely statistical correlation.

The phenomenological correlation may offer the possibility ofextrapolation outside the range of the data it is tested againstand further it may be possible to gain a better understandingof the physical processes involved.

Phenomenological correlations often consist of various math-ematical expressions based on primarily physical principles.The phenomenological model may, however, increase the complexityof the computer programme management and increase the use of

- 28 -

computer time. A compromise between the detailed phenomenologicalmodel and the statistical correlation may therefore be necess-ary. This depends primarily on the sensitivity of the surfacetemperature to the selected correlation. If the sensitivity islow, it may be justifyable to lower the complexity.

A key feature of a well-made computer programme is a high degreeof modularity so that correlatlons and models can be easilychanged.

3.2. Heat transfer in different flow regions

Heat transfer coefficients in single-phase fluids, liquids orgases, åre determined from dimensional analysis and experiments.

Heat transfer coefficients åre calculated from correlations de-termined in this way:

where the dimensionless term on the left side is the Nusseltnumber and the two dimensionless numbers on the right side årethe Reynold and Prandtl numbers, respectively. C1 , C2 and C3åre constants that åre to be determined from experiments undersimilarity conditions. F is a correction factor, which e.g. maytake the length-to-diameter ratio into account.

The other parameters åre defined in the nomenclature list.

Heat transfer in two-phase flow is much more complicated due tothe interacting interfaces between the two phases, liquid andvapour. There åre four types of liquid-vapour interfaces:

1. bubbles in liquid continuous flow2. droplets in vapour continuous flow,3. vapour film in liquid continuous flow, and4. liquid film in vapour continuous flow.

- 29 -

Further, the three different types of heat transfer have to beconsidered:

a. convectionb. conduction, andc. radiation.

Figure 5 gives schematically an impression of the highly com-plex mechanisms involved in the two-phase flow heat transfer.

It is understandable that it is not possible to obtain a singleheat transfer correlation that may cover all the flow regionsshown in Fig. 1 and schematically in Figs. 3 and 4.

Not all the heat transfer mechanisms occur at the same time andthey differ radically in the various flow regions. In mostcases the thermal radiation is negligible.

To a great extent, the physical considerations from structuringsingle-phase heat transfer correlations have been transferredto two-phase flow with appropriate additions even for inter-facial heat transfer.

Superposition of the different heat transfer mechanisms is as-sumed. Nucleate boiling heat transfer, e.g., is correlated asthe sum of the heat transfer by liquid-vapour exchange causedby bubble agitation in the boundary layer (microconvection) andthe heat transfer by the single-phase liquid convection betweenpatches of bubbles (macroconvection). Appropriately determinedweighing factors åre assigned to each term.

In the post-CHF regions with vapour continuous flow the heattransfer is very much dependent on the droplet concentrationand the surface temperature. At relatively low temperatures thedroplets will be able to wet the heating surface when strikingit and thus can be evaporated by direct contact with the sur-face. The heat transfer may be assumed to be a weighted sum of

- 30 -

Bubble

Wall

—— W-L* —

— R-W-L-*-

_ __ — — _

--R-W-V*-

XLiquidContinuous

W-L - 1 -

W V 1

VapourContinuous

/V_

~"L~~i_ — _|\ Yy-R-V - I*~V

'f, Vapour

/ Interfaces

Liquid

Convection

Conduction

Radiation

B BubbleD Droplet1 InterfaceL Liquid

R RadiationV VapourW Wall

FIGURE 5.

- 31 -

wall-to-droplet heat transfer and vapour convection heat trans-fer (transition boiling heat transfer). With a relatively highsurface temperature the droplets åre no longer able to wet thesurface. The heat transfer is decreased, but the presence ofdroplets in superheated vapour will lower the bulk temperatureof the vapour towards saturation temperature due to interfacialheat transfer, thus increasing the heat transfer. Further thetemperature profile of the vapour will be changed causing asteeper temperature gradient close to the heating surface, whichwill also enhance the heat transfer.

Two important points on the boiling curve with their corres-ponding temperatures åre very decisive for the flow region andthus the heat transfer:

1. critical heat flux, and2. minimum film boiling heat flux.

The critical heat flux (CHF) is by far the most important as it,separates normal and abnormal operation with an appropriatesafety margin.

Two mechanisms of CHF åre postulated, departure from nucleateboiling (DNB) in liquid continuous flow and dryout (DO) invapour continuous flow (Fig. 6).

DNB occurs on a heating surface under subcooled or saturatednucleate boiling. Bubbles become crowded in the vicinity of theheating surface and form a moving bubble layer as shown in Fig.6a. When the bubble layer becomes thick enough to impede coolingliquid contacting the hot surface the bubbles will merge into avapour film changing the boiling in heat flux controlled systemsfrom the efficient nucleate boiling to the highly inefficientfilm boiling. Surface temperature excursion is high and fast.Earlier DNB was therefore called fast burnout.

Dryout occurs on a heating surface under forced convective boil-ing. CHF occurs when liquid film becomes too thin and breaks

- 32 -

down into dry patches as shown in Fig. 6b. Surface temperatureexcursion is low and slow. Dryout was therefore called slowburnout in the past.

It is obvious that the two CHF mechanisms cannot be expressedby the same correlation.

The minimum film boiling heat flux and the corresponding minimumfilm boiling temperature is an important parameter in tempera-ture-controlled systems as it separates the high temperatureregion, where the inefficient film boiling takes place, from thelower temperature region, where the more efficient transitionboiling occurs. It thus provides a limit to the initiatingrewetting by emergency core cooling. The heat transfer coef-ficient on either side of the minimum film boiling temperaturecan differ by two orders of magnitude.

As the starting point, more recent studies do not take theminimum film boiling heat flux but rather whether the dropletcan wet the surface or not. The surface can, in faet be rewettedeven if the minimum film boiling temperature has already beenpassed, if the kinetic energy of the droplets perpendicularto the surface can overcome the repulsive forces. This is dis-cussed in Appendix C.

- 33 -

Dryout

Vapour

LiquidAhnulus

\

7

B

Two postulatet! Mechanisms of CHF

A: Departure from NucleateBoiling (DNB)

B: Departure from Forced ConvectiveBoiling (DFCB) or Dryout.

FIGURE 6.

- 34 -

4. COMPARISON OF CORRELATIONS WITH DATA

4.1. Computer programmes used

Another task (SÅK-3) under the SAK-project has been to provideone or more computer programmes suitable for small break LOCAanalysis.

The SA'K-3 work has mainly been concentrated on the Americancomputer programmes RELAP-5 and TRAC(PF1). It is therefore natu-ral to use the heat transfer correlations and the programmeselection logic in these programmes as the starting point for thecomparison. The Norwegian programme NORA has also been used inthe work.

The programme heat transfer packages åre described in AppendixB1.

It cannot be expected that all necessary input data åre measuredin relevant experiments. It is therefore obvious to let the pro-gramme in which the correlation is used calculate these unknownparameters. This^ has been done in some of the comparisons.

However, using large computer programmes like RELAP-5 andTRAC(PF1) in the comparison, especially in transient calcula-tions, include influences from so many physical phenomena andempirical correlations that it cannot be excluded that othertransport phenomena apart from the heat transport may be domi-nant and thus impede the actual aim of assessing heat transfercorrelations.

Separate developed programmes have been used in comparisons ofthe transition boiling heat transfer and to a certain degreealso in the comparison of CHF-correlations in rod bundles.

- 35 -

4.2. Comparisons with data

Several sets of experimental data have been used for the as-sessment of the heat transfer correlations. In all the experi-ments the basic measured parameter was the wall temperature ofthe heater surface. Very minor amounts of information weresupplied about the local prevailing two-phase conditions of thesystem. For this reason some reliance had to be placed in thetwo-phase flow models of the computer programmes that wereused. These two-phase flow models provided the necessary inputparameters to the heat transfer correlations; thus, it wasobvious that the wall temperature calculations were stronglydependent on the adequacy of the two-phase models as well asthe heat transfer correlations. It was an early suggestion inthe project that test sections with simple tubular geometryshould preferably be used in order to have a possibility totrack the two-phase flow calculations. In these experimentsthe boundary conditions for the test section should be welldefined by adequate measurements.

The different experiments selected as test cases åre summarizedin Table 4.2.1. In all the cases the test section was verticallyoriented and the power distributions were axially and in therod bundle cases also radially uniform. (For details of the dif-ferent experiments and of the comparisons, refer to Appendix B2.)

In what follows there will be only a summary of the resultsobtained from the comparison between calculated and measuredparameters.

The three first test cases in Table 4.2.1 were different typesof transients. As pointed out in Appendix B2 it was very diffi-cult to assess the adequacy of the heat transfer package in thecomputer programmes from the results of these test cases.

The basic reason for this was that in transient calculationsthe results åre influenced by a number of models and empiricalcorrelations describing different kinds of transport phenomena

- 36 -

and it is a delicate task to separate the influences from theheat transfer correlations alone. Hence, in the selection ofexperiments it was decided to switch from transient to steady-state experiments concentrating on the Becker cases.

The Becker cases were conducted at the Royal Institute of Tech-nology in Stockholm and reported in (2), and were kindly placedat the projects disposal by Prof. Becker. The test section wasa vertical circular tube directly heated in the tube wall andinsulated on the outer surface. The heated length was 7 meterswith an uniform power distribution. The inner wall surfacetemperatures were determined from thermocouple measurements atthe outer surface and the calculations with RELAP-5, TRAC andNORA were aimed at simulating the axial temperature distributionswhen measured inlet and outlet conditions were applied asboundary conditions.

As there were no options in RELAP-5 nor in TRAC to calculatethe steady state this had to be done by calculating a transientwith time invariant boundary conditions until the solution wasstable. With 20 to 35 axial nodes the CPU-time on a CDC CYBER170-835 for obtaining the steady state in these cases ended upin the range 10 to 20 minutes while the NORAS programme (steady-state version of NORA) required only a few seconds.

From the comparisons between measured and predicted wall surfacetemperatures, it was obvious that the pre-CHF heat transfer cal-culations were quite accurate. For single phase forced convec-tion the heat transfer coefficient was calculated from an ordi-nary Dittus-Boelter type correlation and in saturated boilingregion from Chen's correlation (3) in all three of the pro-grammes.

The DO-predictions were not satisfactory in any of the computerprogrammes. In RELAP-5 the W-3 correlation (4) or the Biasicorrelation (5) was used, but an upper void limit 0.96 was alsoused, and CHF was assumed to have occurred if this value was

TABLE 4 .2 . I.

Test case

Roumy Case 1Roumy Case 2CE/EPRI Case 1 1Becker Case 1Becker Case 2Becker Case 3Becker Case 4Becker Case 5Becker Case 6Becker Case 7ORNL Case BORNL Case CORNL Case HORNL Case KORNL Case N

ORNL Case 0

Type of experiment

Flow transientFlow/power transientBlowdownSteady-state post-DOSteady-state post-DOSteady-state post-DOSteady-state post-DOSteady-state post-DOSteady-state post-DOSteady-state post-DOSteady-state Post-DOSteady-state post-DOSteady-state post-DOSteady-state Post-DOSteady-state post-DOSteady-state post-DO

Geometry

Single tubeSingle tubeSingle tubeSingle tubeSingle tubeSingle tubeSingle tubeSingle tubeSingle tubeSingle tubeRod bundleRod bundleRod bundleRod bundleRod bundleRod bundle

Initial conditions

Pressure(MPa)

14.0014.0015.865.02

10.012.987.023.003.01

13.9912.7612.468.894.388.525.98

Mass flux(kg/m /sec)

1532152735261476502498

100014871005500713334256226806307

Subcooling(°C)

178.193.650.59.8

12.18.9

11.79.7

10.29.5

19.134.838.045.814.322.2

Heat rate( MW/m2 )

2.2672.0100.4591.0150.4570.5620.8150.8690.7650.4050.9100.5600.4170.4400.9400.530

-Jl

- 38 -

exceeded. In TRAC the Biasi correlation or a void limit of 0.97was used. In both RELAP-5 and TRAC calculations the DO was gen-erally predicted to occur too far upstream. In the RELAP-5 casethe DO predictions were also subjected to some flow oscillationsduring the course to steady state, which were influencing theresults. For that reason a separate examination and assessmentof CHF-correlations was made and the results from these effortsåre summarized in Chapter 5.2 and Appendix B4.1.

In order to make it possible to examine the post-CHF heat trans-fer, both RELAP-5 and TRAC were modified so that the DO positioncould be specified through the input. In NORAS another approachwas used: The CHF-value from the correlation was adjusted by afactor to obtain the measured DO position. From the cases, sorecalculated it was obvious that the predicted post-DO walltemperatures were significantly lower than the measured onesand also that the calculation of the nonequilibrium effectstypical for the post-DO region was inadequate.

Both NORAS and RELAP-5 were modified in order to have thepost-DO calculations improved. As the nonequilibrium effectsåre basically governed by the mass transfer rates between thephases it is obvious that a decrease of the vapour generationrate will increase the vapour temperature thus allowing for thenonequilibrium conditions to be more pronounced. For that reasona new vapour generation model (6) was implemented for the post-DO region in these programmes. In RELAP-5 also the heat trans-fer models were modified so that the heat was transferred fromthe wall to the vapour phase and then from the vapour phase tothe droplets. The calculated results after these modificationswere substantially improved and a satisfactory agreement be-tween the measured and calculated post-DO wall temperatureswas obtained.

4.3. Experiences using the computer programmes

During the work a number of difficulties have been encounteredwith the programmes. The main ones have been concerned with

- 39 -

the numerical methods used in RELAP-5 and TRAC. These programmesturned out to be inefficient in the calculation of steady statetests. The implicit methods used have been more effective by afactor of 10...100 in the present test cases.

Another group of difficulties has been caused by the constitu-tive models. Because RELAP-5 and TRAC åre primarily intendedfor transient calculations, the constitutive models have notbeen suitable for steady-state situations. An example is theway the critical heat flux is calculated in RELAP-5. Fur-thermore, many set of correlations contain discontinuities,which may cause troubles for the numerical method. In somecases it is possible that no steady-state solution can be foundby RELAP-5.

The most important experiences using the computer programmesåre, however, concerned with the accuracy of the correlationpackages used. The main emphasis has been paid to wall heattransfer correlations. During the SAK-5 project it appearedthat also the friction correlations and especially the inter-facial heat transfer correlations used in the system programmeswere poorly tested. The interfacial heat transfer correlationsåre closely connected with wall heat transfer correlations andhave a strong effect on wall surface temperatures in the post-dryout region. The experiences using computer programmes åredescribed in more detail in Appendix B3.

4.4. Comparisons using separate programmes

The test section in the vast majority of experiments is made asdirect resistance heated tubes with no filler material in thetubes. The thermal capacity of such a test section is muchsmaller than in nuclear reactor fuel rods. The transient be-haviour, e.g. in a simulation of a LOCA will not be correctlyreproduced, the velocity of the rewetting front will be toohigh and the transition boiling region is hardly reproduced.It is possible to make electrical resistance heaters that can

- 40 -

simulate the stored heat, but the costs of such heaters årehigh, at least 50 times higher than a simple resistance heatertube.

Further, compared to the other flow regions, the transitionboiling flow region is short both in extent and time for run-through and difficult to measure in a larger integral post-CHFexperiment.

Rewetting and transition boiling heat transfer åre thereforeexamined in experiments made for this special purpose, i.e.special considerations åre taken to make the experiment tem-perature controlled, e.g. use of thermal storage block in con-nection with the test section or the water is boiled by indi-rectly heating by another fluid, e.g. hot mercury as in theEPRI-experiment.

Recalculation of such experiments calls for separately devel-oped smaller computer programmes.

An advantage of such programmes is that several heat transfercorrelations may be compared with experimental data. It is thennecessary, however, to assume that the correlations used inthe prediction depend only on local parameters, i.e. ratherthan on the upstream history. It must be foreseen that shouldmore realistic models be developed, the degree of nonequilibriumat any axial location must be the result of a historicallydeveloped state dependent on the upstream competition betweenthe heat transfer mechanisms wall-to-vapour, wall-to-dropletand vapour-to-droplet.

- 41 -

5. DISCUSSIONS AND RECOMMENDATIONS

5.1. Nucleate and forced convective boiling

Highly accurate heat transfer correlations in the nucleateboiling and forced convective boiling flow regions åre notrequired in order to calculate heat transfer during a LOCA(7). The reason for this is that heat transfer in theseregions is very efficient and should not be a limiting factorconcerning the behaviour of fuel and cladding during a LOCA.For using heat transfer correlations in steam generators inPWR systems, the situation is somewhat more restrictive.During a LOCA the heat flow in the steam generators may changedirection and cause steam generation in the recirculationloops - which strongly influences the flow of coolant throughthe loops.

In single-phase forced convection any well-known heat transfercorrelation may be used, e.g. Dittus-Boelter.

In the nucleate boiling flow region, most heat transfer correla-tions can be written in the following form:

- B1(P) - (TW-TSAT)B2

= hNcB

The heat transfer correlations that seem to give the best fitto experimental data have a value close to 2.0 for B2. The cor-relation by Stephan and Auracher (Table A1. II) has this value-and is recomrnended to be used for both the reactor core andsteam generators. For the reactor core, a somewhat simplified

- 42 -

version of the Chen correlation is considered accurate enough.

5.2. Critical heat flux

The results of the literature search åre given in Appendix A2and the outcome of some recent assessments of CHF correlationsin rod bundle geometries is summarized in Appendix B4.1.

Leung(22) has demonstrated that an appropriate steady state CHFcorrelation was adequate for the prediction of CHF onset duringa wide range of transients. He also indicated that the localcondition hypothesis can be used for CHF predictions. Thisraethod is most advantageous in transient analyses. It is verydifficult to define an adequate boiling length at each instanceduring the course of a transient, which is a requirement whenother methods åre employed.

In Appendix A2 it is recoramended to use Griffith-Zuber correla-tion for the low mass flux range:

-240 < G < 100 kg/m2s.

Outside this mass flux range the Biasi and CISE-4 correlationswere found to be equally good possibilities. However, it has tobe emphasized that this outcome was based on the comparisonbetween the measured and predicted time to CHF during differentkinds of transient in round-tube or scaled-rod bundle test sec-tions. When Biasi and CISE-4 correlations were used for predic-tion of the CHF in full-scale rod bundle steady-state experi-ments they were found to be very non-conservative (cf. AppendixB4.1) . This was attributed to the development of these twocorrelations from single-tube data. There were no provisionsfor incorporating the effects of unheated wall surfaces andinternal rod-to-rod power distributions. As would be expected,the rod bundle CHF correlations were found to be much moreaccurate when predicting the CHF in this type of geometry, andit was recommended that the Becker rod bundle CHF correlation

- 43 -

be used within the following parameter ranges:

Pressure 3.0 - 9.0 MPa

Mass flux 400 - 3000 kg/m2s

Heat flux 0.5 - 3.0 MW/m2

For mass fluxes between 100 and 400 kg/m2s an interpolation ofthe Becker and the Griffith-Zuber correlations has to be made.

Above 9.0 MPa it is not clear which correlation to use. Notesting of CHF correlations in this pressure range has beenperformed within the project, and no firm recommendation canbe given. In the literature several possible correlationsåre reported, e.g. the correlation proposed by EPRI (8) andthe one by Bezrukov et al. (9), but these have to be morethoroughly tested and validated before drawing any conclusions.

Also, the situation in the low-pressure range (P < 3.0 MPa) isnot very well examined. Due to the lack of rod bundle experi-mental CHF data for these low pressures no assessinents of CHFcorrelations have been made and thus no recommendations can begiven. It is obvious that there is a strong need for moreexperimental data and analysis in this low-pressure range.

5.3. Transition boiling

The experimental data used in this comparison åre primarily inthe vapour continuous flow region and only very few in the tran-sition flow between vapour and liquid continuous (churn/slugflow).

The correlations selected for comparison (except the correlationby Hsu) were developed primarily for the dispersed flow regionin vapour continuous flow. It cannot be expected that the cor-relations can be used in the inverted annular flow region, i.e.

44 -

liquid continuous flow.

The comparison shows the necessity of taking thermodynamic non-equilibrium into account.

The comparison also shows that the direct liquid-wall contactheat transfer is important and has to be accounted for espe-cially in regions near the CHF location. This is in contra-diction to the widely used assumption that the contact heattransfer is negligible.

Much more work is needed, however, before transport phenomenain transition boiling can be described.

It is the purely empirical and simple heat transfer correlationby Bjornard and Griffith (11) that relates the test data best;therefore/ it must be recommended for use until better phenom-enological correlations or models åre developed.

The inverted annular flow region in liquid continuous flow hasnot been examined.

5.4. Rewetting

The rewetting process means a reversal from film boiling condi-tions after DO or DNB back to nucleate boiling and the maininterest concerning the phenomena is connected with large LOCAreflooding or spray cooling.

Two possible methods may be seen for the modelling of the rewet-ting front:

The two-dimensional heat conduction equation may be solved nu-merically and the moving mesh techniques åre used to split theheat structure around the rewetting front into finer meshes. Thenumerical inaccuracy is avoided if the finest meshes in axial di-rection åre shorter than 0.001 mm. In moving-mesh techniques theheat transfer correlations åre used for the nucleate boiling,

- 45 -

critical heat flux and transition boiling. The moving-mesh tech-niques should not be used if the computing time consumption islimited.

The second possibility is to apply a mathematical correlation forthe rewetting velocity. Then the formula of Dua and Tien is re-commended^ _^

0.5Pe = Bi /. „ .„ Bi1 + 0.40

ew*(9w~1) \ 6w*(9w~1)

6-p'c-u h«6 T~TSATPe =—————;Bi = —— ; e = ————; ew = Ø(TW)k k TO-TSAT

The fitting parameters of the mathematical formula åre the heattransfer coefficient h in the Biot, number Bi and the rewettingtemperature T0 in the nondimensional temperature. The recommen-ded heat transfer coefficient is the critical heat flux of Zubercorrelation divided by the temperature difference (ATg^T =TCHF~TSAT)• this difference is calculated from the wall tempe-rature during nucleate boiling determined by the Chen cor-relation. The slowing down of the rewetting due to void fractionis taken into account by the factor (1-oc) proposed by Griffith.Two possibilities åre recommended for the rewetting temperature:the use of minimum film boiling temperature or a simpler formulalike: TQ = TSAT + 160 + 6'ATsub .

5.5. Film boiling

The film boiling region can be divided into basically two flowsub-regions: inverted annular flow and dispersed droplet flow.The development of these sub-regions is strongly influenced bythe prevailing pre-CHF region which can be determined from aflow region map.

For the inverted annular flow the heat transfer mechanisms åreas yet not very well understood. Until more research sheds lighton these issues a simplified approach using a modified Bromleycorrelation is recommended to calculate the wall heat transfer:

- 46 -

q" = hFB.(Tw-TSAT)

hpB = 0.62 •1/4

Xc = 2 n

The parameter range for this correlation is

Pressure 0.1 - 0.7 MPa

Wall heat flux 30 - 130 kW/m2

Subcooling < 78 K

Velocity < 0.3 m/s

Void < 0.4

The transition of inverted annular flow to dispersed dropletflow may be related to a critical Weber number. When thisWeber number is exceeded the liquid core in the inverted annularflow will break down into slugs and droplets. The Weber numberis defined as

Wetr

and the critical We-number according to this definition has therange 10-20.

For the dispersed droplet flow different approaches have beenadopted when calculating the wall heat transfer. The most prom-ising seems to be the phenomenolog ical approach in conjunctionwith a separate fluid model. Different heat transfer modes årethen identified and described as well as the interfacial trans-port phenomena. This approach is also very well suited forthermohydraul ic programmes like RELAP-5 and TRAC.

- 47 -

In the film boiling region it is usually assumed that theradiation and wall-to-liquid heat transfer terms åre negligiblecompared with the wall-to-vapour terms. This latter heat transfercan be calculated according to the revised version of themodified CSO (Chen-Sundaram-Ozkaynak) correlation:

q" = h-(Tw-Tv)

h = hmod CSO d+Fs)(1+0.8/(L/D))

25010.69

XA

0.49Re-0.55

hmod CSO = -<(

-0.1

= 3.48 - 4-log 10

cvf

f 11 + 9'35 1L D Rev /To" J

The basic interfacial processes åre dealt with in Chapter 5.6.

When the flow region is single-phase steam flow, where thesteam may be superheated, the well-proven correlations of Dittus-Boelter's type can be used to calculate the heat transfer coef-ficient. The Sieder-Tate correlation is one example of thistype:

q" = h-(Tw-Tv)

0.14

The revised version of the modified CSO correlation seems tohave a smooth transition to this correlation when XA approachesunity.

- 48 -

For very low flows natural convection may become a significantcontributor to the total heat transfer. For turbulent naturalconvection heat transfer to single-phase vapour the followingcorrelation can be used:

P2f.g.p f.(T -T ) V30.13.kyf -*± ——— -. ————

where the properties åre evaluated at film temperature.

5.6. Interfacial heat transfer

When thermodynamic nonequilibrium between the phases is assumed,a constitutive model is needed for the interfacial heat transfer.The way in which the constitutive model is applied depends on theassumptions made in the hydraulic model. When a two-fluid modelis applied two constitutive equations åre needed, one for theheat transfer from the interface-to-vapour phase (Qig) and an-other from the interface-to-liquid phase (Qii). These åre re-lated to the interfacial mass transfer as

Qig+QiA

Hfg

where Hfg is the latent heat of evaporation.

If simplifying assumptions have been made in the hydraulics thenumber of interfacial constitutive equations decreases. The u-sual assumption is that one of the phases is saturated while theother phase is in thermodynamic nonequilibrium. In that case onlyone equation for the interfacial energy transfer must be speci-fied. Usually the model is applied for r. Because there is alack of experimental correlations the same approach is veryoften used also with the two-fluid model. The interfacial heattransfer rates åre expressed as:

Qik = hik*(TSAT-Tk)

- 49 -

where T is temperature, h^ is a kind of heat transfer coef-ficient (Joule/m3'S'°C) and the subscript k is either g or i .When this equation is used the phase can be forced to be satu-rated by applying a large interfacial heat transfer coefficienthik. In some cases the interfacial heat transfer is closelyrelated to the wall heat transfer. One example is subcooledboiling. In this case a separate wall boiling model must beapplied, because when the average fluid is subcooled, no eva-poration is predicted through the above equations. If rw isthe amount of wall flashing, the total flashing rate is expres-sed as:

rtot = rw + r

where r is calculated from the above mentioned equation. r isnegative (condensation) in the case of subcooled boiling. Inpractice it is very difficult to model rw so that the totalflashing rate is correct. For example, the TRAC(PF1)-programmewas unable to predict any subcooled boiling in the test casesanalyzed in the SAK-5 project.

Another case where the interfacial heat transfer rate has astrong effect on the wall heat transfer is post-dryout heattransfer. In the post-dryout flow region the interfacial areabetween the phases is small and the heat transfer coefficienthig is low. Consequently, the vapour temperature is increasingin that region, which results in higher wall surface tempera-tures if the wall heat transfer coefficient remains constant.Encouraging results have been obtained in the SAK-5 projectby applying interfacial heat transfer models in the post-dryoutregion. Another approach in the post-dryout region would be themodification of the wall heat transfer coefficient so thatbetter agreement with experimental surface temperature is ob-tained. In faet, this is the only way if equilibrium betweenthe phases is assumed. The use of a nonequilibrium assumptionenables the more realistic prediction of the wall temperaturedistributions.

- 50 -

Although the interfacial heat transfer has an important role intwo-phase flow predictions, relatively few empirical correla-tions exist at present. In the SAK-5 project only two areashave been studied and only preliminary results have been ob-tained. These results cover the area of flashing and post-dryoutflow region.

The flashing rate is important in the prediction of the pressurerecovery following a rapid depressurization and in the predic-tion of the liquid superheat in quasi-steady flow. The latteris important in the calculation of critical flow. Severalflashing correlations have been tested (14). According tothe test cases performed the experimental correlation of Baueret al. (15) gave the best agreement with experimental data.This correlation can be expressed for h^ as

where a is void fraction, Cp is specific heat and p^ is liquiddensity. The time constant T is defined as

660

(a+a0)(u+u0)2 /F

where u is liquid velocity and P is pressure in På. This cor-relation is valid in the range of 0.01 < <x < 0.96 and 5 m/s <u < 54 m/s, when ao = uo = 0. However, because there åreno other suitable correlations, it is suggested that thiscorrelation is extrapolated outside its validity limits. Forthis purpose the constants oco and uo have been determinedto be 0.003 and 4 m/s. In this form the correlation predictscritical flow data with good agreement. In the prediction ofthe pressure recovery following a rapid depressurization, theagreement seems to depend on the flow area. Relatively goodpressure history is predicted with medium-size pipes. In thecase of Edward"s pipe test, the predicted pressure recoveryis too slow and in the case of a large vessel it is too fast.However, this kind of uncertainty has not such a vital impor-tance as has the uncertainty in the calculated critical flow.

- 51 -

Another area that has been studied in the SAK project is thepost-dryout flow region. Calculations have been performed usinqNORAS and RELAP-5 programmes, which both gave good results. Thecorrelation used for r has been developed by Webb et al. (6)

-1.1T = 1.32 _

]2 (1-a)2/3-kv. (TV-TSAT)

Pv-D'a'Hfg

where Pc is critical pressure, G is mass flux, XA is actual qua-lity, kv is thermal conductivity of superheated vapour, D ishydraulic diameter, and a is surface tension. This correlationhas been used only for the post-dryout region. Ih that regionQig » Qilf which makes it possible to express the correlationfor hin as

hig = 1.32--1 .1

G'XA (1-

pv«a'D

This correlation has been extensively compared with experimentaldata elsewhere (16). According to the recent studies the corre-lation gives a mass transfer rate just after the DO positionthat is too low. Because of this a modified version of it hasbeen developed (17). The increased vapour generation rate inthis "near-field region" is referred to some sputtering effectswhen the wall liquid film is driven violently off (or reformedby droplet-wall contact) at the CHF-location, i. e. this is notreally an interfacial heat transfer. At present, a final eva-luation of the correlation as yet has not been made.

In calculating the interfacial heat transfer one possibilityis to use the above equations for h^^ and h^g whenever eva-poration occurs. This is justified by the simple faet thatthere åre no better correlations. Furthermore, usually eitherQig or is dominant in the calculation and the extra-polations of the other correlations outside its range åre notso harmful. It is obvious that a lot of work must be performedin the future with the interfacial heat transfer mechanism. Inthis context only two recommendations can be made. However, thecorrelations recommended åre not yet thoroughly tested; theiruse with a wall boiling model especially remains to be studiedin the future.

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6. CONCLUSION

It is both natural and rather obvious to test heat transfercorrelations in the environment in which they åre to be used,i. e. the computer programmes TRAC, RELAP-5 and NORA. Theadvantage is that parameters not measured in the experimentåre calculated under conditions in the programme which oughtto correspond to reality in the experiment.

It was, however, not possible in the transient calculations toassess the adequacy of the heat transfer package in the indi-vidual programmes. It can not be excluded that other transportphenomena (subcooled void, slip, thermodynamic nonequilibrium)and empirical correlations veil the actual aim, viz. toassess the heat transfer correlations.

The general idea, to use the computer programmes in the com-parison, was retained, but it was decided to make a switch inthe selection of experiments from transient to steady state,simple experiments.

The accuracy of heat transfer correlations in pre-CHF regionsi.e. the nucleate boiling region and the forced convectiveboiling region does not have to be very high for the purposeof calculating heat transfer during a LOCA. The heat transferin these regions is very efficient and should not be a limit-ing factor for the fuel and cladding during a LOCA.

The critical heat flux (CHF) calculations were carried outwith the W-3 correlation (4) (primarily a DNB correlation)in RELAP-5 as well as the Biasi correlation (5). The pre-dicted dryout locations were too far upstream (up to ~ 3 mat low pressure). The CHF were in some cases determined by acutoff void limit of 0.96 when the Biasi correlation wasused.

- 53 -

The results from TRAC were fairly accurate except at low pres-sure. TRAC makes use of the Biasi correlation, but in none ofthe cases did the correlation determine the locus of dryout.An arbitrarily chosen cutoff void limit of 0.97 caused dryout.

The NORAS calculations used three different CHF-correlations,Biasi, CISE-4 (24) and Becker (64). Biasi and Becker corre-lations predicted dryout too far downstream while CISE-4 corre-lation predicted dryout too far upstream at high quality andtoo far downstream at low quality.

It was therefore necessary to freeze the locus of CHF at themeasured location in order to compare the surface temperatures.This comparison was not good in any of the prograinmes used.The calculated surface temperatures were too low in RELAP-5and TRAC indicated an interfacial heat transfer that was toohigh. NORAS gave too high surface temperatures,i.e. too lowinterfacial heat transfer.

This can be seen from a single calculation using NORAS and 5calculations using RELAP-5 in Pigs. B2.21-B2.27. In twoof the RELAP-5 cases the interfacial heat transfer was sohigh that no vapour superheat was calculated (the liquid andvapour post-dryout temperatures were about the same).

The test section was an electrically heated tube with a verylow thermal capacity i.e. a typically heat flux controlledexperiment. The thermodynamic nonequilibrium effects åretherefore primarily governed by mass transfer between dropletsand vapour due to interfacial heat transfer. A decrease inthe vapour generation rate will increase the vapour tempera-ture under equal conditions, thus allowing the thermodynamicnonequilibrium to be more pronounced.

The programmes were modified by implementing a recently deve-loped vapour-generation model by Chen (6). Recalculated re-sults were substantially improved and a satisfactory agree-ment between measured and calculated post-dryout surface tem-peratures was obtained.

- 54 -

From these examinations, together with the examinations of thetransition boiling heat transfer with a separate computer pro-gramme, it is obvious that more realistic and phenomenologicalheat transfer models have to be developed. It must be recognizedthat the degree of thermodymamic nonequilibrium at any axial lo-cation is dependent not only on local conditions but especiallyon the upstream competition between the heat transfer mechanismswall-to-vapour, wall-to-droplet and vapour-to-droplet.

Up to now this report treated the post-CHF region in moreindependent chapters, transition boiling heat transfer, rewett-ing, interfacial heat transfer and film boiling with and with-out droplets. To get realistic models the transport phenomenahave to be considered in more detail and the post-dryout regionmay be treated as one region where the dividing point betweentransition boiling and film boiling is not the minimum filmboiling temperature, but rather the point where the droplet canwet the surface or not. The surface canyin fact/be rewettedeven if the minimum film boiling temperature has been passed,if the momentum of the droplets perpendicular to the surface canprevail over the repulsive forces due to evaporation at the wall.The pro j eet decided to touch upon these phenomena in a some-what more detail and the results åre discussed in Appendix C.

With respect to the discouraging results of critical heatflux calculations, the project decided to make a closer elabora-tion of 4 relevant CHF-correlations: Barnett, Becker, CISE-4 andBiasi using results from full-scale rod bundle experiments.The results indicate that Biasi and CISE-4 correlations, whichåre used in computer programmes like RELAP-5 and TRAC, cannotpredict the CHF-conditions with adequate accuracy. An explana-tion is believed to be that these two correlations åre developedfrom single tube data and have no provisions to incorporatethe influence of unheated surfaces and internal rod-to-rodpower distribution. The two other CHF-correlations åre de-veloped for rod bundle geometries and correlate the experimentaldata more accurately. It is therefore recommended that thesecorrelations instead of Biasi and CISE be used.

- 55 -

NOMENCLATURE LIST

A Area m2C Specific heat capacity joule/kg°CCo Distribution parameterd Diameter droplet mD Diameter mE Entrainmente Internal energy joule/kgf Friction coefficientG Mass flux kg/m2«sg Gravitational constant m/s2h Heat transfer coefficient W/m2ocH Enthalpy joule/kgHfg Latent heat of evaporation joule/kgj Volumetric flux (superficial velocity) m3/m2sk Thermal conductivity W/m°CL Length mLC Characteristic length mM^k Generalized interfacial drag force N/m3

n Normal vectorP Pressure PåPc Critical pressure Påq" Heat flux W/m2Q Heat flow rate Wattr Radius droplet mR Gas constant joule/kg°CT Temperature °Ct Time su Velocity m/sv Velocity m/sV Volurne m3

XA Quality (nonequilibrium)XE Quality (equilibrium)y Distance normal to wall and positive

towards centre of channel m

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Greeks

a Void fractionP Volumetric expansion coefficient

(- 1/p (5p/8T)p) 1/°C6 Wall thickness or boundary layer

thickness mr Vapour generation rate kg/m3se Surface roughness mK Thermal diffusivity m2/sli Dynamic viscosity kg/m«s£ Integral variable Sp Density kg/m3a Surface tension N/mTZ Shear stress N/m3

•czz Viscous or turbulent stresses N/m3

Subscripts

b BoilingCHF At critical heat fluxd Droplete Equivalentf Fluid (liquid)FB Film boilingFF Far field regiong Vapour (saturated)i Interfacek Generalized phase indexH LiquidLC Liquid contactMFB At minimum film boilingNF Near field regionNcB Nucleate boilingNU NonuniformSAT At saturationTB Transition boilingT TotalV Vapour (superheated)

- 57 -

Dimensional groups

h'6Bi Biot number

Fr Froude number

kw

g-D

P2.(3-9(TW-T)D3

Gr Grashof number __________

h«DNu Nusselt number __

k

Pe Peclet number Re»Pr

Cp-nPr Prandtl number

G-DRe Reynold number __

- 58 -

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- 62 -

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- 65 -

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