Neutronic and thermal hydraulic design of the graphite moderated helium-cooled high flux reactor

Nuclear Engineering and Design 139 (1993) 221-233 221 North-Holland

Neutronic and thermal hydraulic design of the graphite moderated helium-cooled high flux reactor

Peng H o n g Liem and Hiroshi Sekimoto

Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152, Japan

Received 6 April 1992, revised version 22 June 1992

A new design concept for a high flux reactor was investigated, where a graphite moderated helium-cooled reactor with pebble fuel elements containing (Z35U, 23Su)o2 TRISO coated particles was taken as its design base. The reactor consists of an annular pebble bed core, a central heavy water region, and inner, outer, top, and bottom graphite reflectors. The maximum thermal neutron flux in its central heavy water region as high as 10 is era -2 s -1 with thermal neutron spectral purity of more than two orders of magnitude and a large usable volume of more than 1,000 liters can be achieved by (1) diluting the fissile material in the core and (2) optimizing the core-reflector configuration. The in-core thermal-hydraulic analysis was done to obtain adequate information about the coolant flow pattern and pressure distribution, core temperature profile, as well as other safety aspects of the design. To protect the reactor during off-normal or accident events, a large margin of temperature difference between the operating fuel temperature and the fuel limit temperature is confirmed by lowering the coolant inlet and core rise temperatures.

1. Introduction

An alternative design concept for a high flux reactor (HFR) has been proposed by P.H. Liem et al. [1] and its feasibility is being investigated. Instead of a water- cooled reactor, a graphite moderated helium-cooled reactor with pebble fuel elements containing (Z35U, 23SU)Oe TRISO coated particles was taken as the design base. To provide higher values of thermal neu- tron flux with a better spectral purity and larger usable volume, further calculation and refinement of the de- sign have been continuously worked, Those efforts are also accompanied by the in-core thermal-hydraulic analysis to provide adequate information of the coolant flow pattern and pressure distribution, core tempera- ture profile as well as other safety related aspects of the design.

This paper presents the methods, procedures and results of the above design calculation and refinement. Section 2 reviews briefly the fundamental physics be- hind the design concept as well as objective and proce- dures for refinement and optimization of the HFR design. In Section 3, the thermal-hydraulic properties of the core containing pebble fuel elements and related experimental data are discussed, and numerical meth- ods for solving the steady-state thermal-hydraulic and

flow problems inside the core are presented. In Section 4, the results of the calculation and refinement of the design are presented and discussed. Section 5 provides the conclusion of the present work.

2. Neutronics

2.1. Design objectives and procedures

The main purpose of the high flux research reactor is to provide a neutron flux density as high as possible having an energy spectrum, space dependence and usable volume which are optimized to meet the user's or experimenter's needs. Furthermore, the reactor fa- cility must be able to be operated easily, safely and uninterruptedly.

The high flux reactor design objectives, procedures and constraints are tabulated in table 1. The design procedures are divided into neutronic and thermal-hy- draulic parts, where for each part, the design objectives and constraints are defined. However, in the present work, rather than concluding with only one optimal design, we search optimal ranges of various design parameters which give high values of figure of merit (FOM) and desirable thermal design results. The re-

0029-5493/93 /$06 .00 © 1993 - Elsevier Science Publ ishers B.V. All rights reserved

222 P.H. Liem, H. Sekimoto / Graphite moderated helium-cooled HFR

Table 1 Design objectives, procedures and constraints

Design Neutronic Thermal

Objective High values of FOMs Low initial fuel temp. (cf. table 2)

Procedure 1. Minimize fissile loading 2. Optimize core-reflector configuration

Constraint 1. Criticality 2. Negative fuel temp. coefficient

1. Lowering coolant inlet and core rise temps. 2. Increasing sys. press. 1. Min. coolant inlet temp. 2. Max. system pressure 3. Max. power density

suits of the calculation which show the behavior of the design parameters in those ranges provide valuable information for the final design of the I-IFR.

The neutronic design objective is to obtain high values of FOMs shown in table 2. The FOMs are used to provide guide lines of the present I-IFR design, and to evaluate the design qualitatively and quantitatively.

The first FOM, i.e., the maximum thermal neutron flux, gives the most important aspect of the I-IFR performance. The second FOM, i.e., the maximum thermal neutron flux per specific power, is considered important since it relates the neutronic to the thermal aspect of the design. In this FOM the power density (Q) is chosen rather than the reactor power (P) as the power density imposes severer constraints on the ther- mal design than does the reactor power. The third FOM indicates the volume outside the core containing high values of neutron flux (~bth> 80% th ~bm~) which

Table 2 Figures of merit for the HFR design

FOM Symbol

1. Max. therm, neutron flux ~maxth

2. Max. therm, neutron flux ~bthma x

Power density Q

3. Usable volume

4. Therm. neutron spectral purity

5. Accessibility of the usable volume

Vuse (~th > 80% ~b~)

S th r rle~l,(r, E) dE dV . ' , J~ 0

fv, fEEty'~&(r, E) dE dV

A diameter of exp. region

height of exp. region

can be effectively used for neutronic experiments. The fourth FOM shows the purity of the thermal neutron flux inside the usable volume. The last FOM is used to evaluate the accessibility to the usable volume. The accessibility to the usable volume may be judged quali- tatively by considering: firstly, its geometry, i.e., the height and diameter of the region; and secondly, the material used in the region. The geometrical aspect of the region has to be considered since various appara- tuses are expected to be inserted or removed from the region. In the present design the ratio of the diameter and height of the experimental region is expected to show qualitatively easiness for accessing the internals of the usable volume.

The HFR neutronic design procedure consists of two parts. The first part concerns the effort to raise the thermal neutron flux in the core. It can be achieved by diluting the fissile loading as low as possible. The idea is clearly shown through the relation between the reactor power, fissile density and neutron flux (nomenclature is given in the last page),

P=f fEC,~(r)af,(r, E)•(r, E) dE dV. (1) " Vcoro" i

For fixed values of P (or Q ffi P/Vcor~) and core vol- ume (Vcore), reducing the fissile atomic density (Nj) results in an increase of the neutron flux (d)). Further- more, the core moderation ratio (MR), i.e., the carbon to uranium atomic density ratio, increases and the core's neutron spectrum becomes soft. The soft spec- trum of the core drives the whole reactor spectrum to be softer. Another consequence of using a low fissile density is that the core is more transparent to fast neutrons, since the migration area is enhanced. This indicates that optimization of core-reflector geometry is needed to provide the optimal neutron spectrum and volume outside the core for neutronic experiments. Further explaination is given in the following discus- sion.

P.H. Liem, H. Sekimoto / Graphite moderated helium-cooled HFR 223

(a) 2.5

2.0 u} o ,~ 1.5

=

1.0

2 0.5

0.0 I I 10 TM 1010

U-235 ATOMIC DENSITY ( /cc)

I 1020

Fig. 1.

o(b) 1.2

2 1.0

0.8

2 0.6

~ 0.4

"~ 0.2

0.0 10 is 1019 1020

U-235 ATOMIC DENSITY ( /cc)

10 5

10 4 o m

i0 a 8 102 -g

E

Some important results of the neutronic cell calcu- lation are presented in figs. l(a) and (b). (The discus- sion of the cell calculation is given later, and the calculation conditions are summarized in table 3). In fig. l(a), the infinite (or cell) multiplication factor k® together with its constituents (commonly known as four factor formula, k® = ~Tepf) are drawn as function of fissile atomic density (235U). In fig. l(b), the relative absorption rates of the most important nuclei, MR and the ratio of thermal to fast neutron flux are plotted as well.

Table 3 Standard data for pebble fuel element cell calculation

Coated panicle fuel Kernel material (235U/23Su)o2

fissile enrichment (%) 20

diameter (p,m) 500 density (g/cc) 10.9

Coatings material PyC/PyC/SiC/PyC (from inner) thickness (/zm) 90/40/35/35

density (g/cc) 0.9/1.85/3.2/1.85

Pebble fuel element Fuel matrix material graphite

diameter (cm) 5 Outer layer material graphite

thickness (cm) 0.5 Fuel element diameter (cm) 6

Few group structure Upper bound Lower bound

(eV) (eV) Range

107 1.11 × 105 fast fission 1.11 × 105 2.90 × 10 z slowing down 2.90 × 101 2.38 resonance 2.38 ~ thermal

As the 23SU atomic density increases and the MR decreases, the thermal utilization factor ( f ) and reso- nance escape probability factor (17) show reverse be- haviors. The increasing absorption rate of uranium and decreasing absorption rate of carbon in the core ex- plain the behavior of f value. An increasing absorption rate of 23SU results in smaller values of p. The change of the neutron spectrum results from the change in MR as is clearly seen in fig. l(b). In turn the change of the neutron spectrum affects the fast fission gain (~).

To achieve high values of the conversion ratio and fuel bum-up, power reactors are in general designed with fissile atomic density values located in the right side of the k® peak. In contrast, the design concept explained through eq. (1) above shows the 235U of the HFR design must be located in the left side of the k® peak, in which the fissile atomic density is low, the MR is high, and the neutron spectrum is soft. The high degree of fuel burn-up is readily solved since pebble bed reactors have an on-line refueling capability. An- other advantage of the on-line refueling capability is that no excess reactivity for burn-up compensation is needed for the design, even though the in-core fissile inventory is held to a minimum. Hence we may elimi- nate the possibility of a severe reactivity accident for the design.

Of course there are limitations for lowering the fissile atomic density. These include the criticality con- dition. The decreasing of k® as we go in the decreasing direction of the 235U atomic density is mainly due to the larger absorption rate of carbon (cf. fig. l(b)), reflected in the lower values of f shown in fig. l(a).

Another constraint in the neutronic design proce- dure shown in table 1 is the negative fuel temperature coefficient. From safety point of view, this constraint is essential. In fig. 2 the fuel temperature coefficient of the HFR design is shown where the fissile 235U atomic

224 P.H. Liem, H. Sekimoto / Graphite moderated helium-cooled HFR

0

t.)

(10 -5 Ak/k/* K) ]

]

I-- 400 6 0 800 I000 1200 1400 1600 "

FUEL TEMPERATURE (°K)

Fig. 2.

density is 2 × 101S/cc. The temperature coefficient is negative for all operating temperature regions.

In this design we use a 20% enriched uranium, even though a highly enriched uranium (> 90% 2aSU) gives a slightly higher maximum thermal neutron flux. A highly enriched uranium fuel is not a necessary condi- tion for the design proposed, as we do not aim at a very small or compact core with a large excess reactiv- ity for burn-up compensation. Also, the medium en- riched fuel used in this design provides larger negative fuel coefficients than does a highly enriched one.

The second part of our neutronic design procedure relates to the effort of determining the optimal core- reflector configuration to produce high values of ther- mal neutron flux with a good spectral purity and large usable volume outside the core. Here, we propose the core-reflector configuration shown in fig. 3. The reac- tor consists of a pebble bed annular core cooled with a downward forced flow of helium coolant, a central heavy water region confined in a tank (for experimen- tal use), and inner, outer, top and bottom graphite reflectors. As shown later in the subsequent discus- sions, the highest thermal neutron flux with a high thermal neutron spectral purity and large usable vol- ume is expected to be obtained in the central heavy water region. Thermal neutron flux of more harder spectra (containing epithermal neutrons) is expected to be obtained in the inner graphite reflector region. Thermal neutron flux of moderate values is also avail- able in a large volume in the outer graphite reflector region. From this region several thermal neutron beams can be installed. As shown in fig. 3, the control and safety rods are also located in this region. The rods are located outside the core to eliminate (1) the possibility of rods' stuck event when the rods are inserted into the core, and (2) the possibility of pebble fuel elements failure by thrust of the inserted rods. By placing the control rods in the outer reflector region, Le., outside of the core, large worths of reactivity may not be

obtained. However, the pebble bed core does not need a large excess reactivity for burn-up compensation. The function of the control rods is only for fine power regulations. The safety rods are used in off-normal events to rapidly bring the reactor to shutdown condi- tion. The central heavy water and inner graphite re- flector regions have higher neutron importances than does the outer reflector region and safety rods could be also located there. However, by locating the safety rods in those regions, the usable volume for neutronic and irradiation experiments as well as easiness for accessing those regions has to be partly sacrificed. Therefore, the safety rods together with the control rods are located in the outer reflector region.

The central heavy water region is essential for the design to obtain high values of FOMs. By providing this region the following items were obtained. (1) Heavy water in the experimental region provides

an adequate thermalized/soft neutron field in that region.

~\-..-,

, . \ \ \ TOP

:o~o~ ~

BOTTOM

z

e

I

Fig. 3.

control rod

safety rod

irrad~tion tube

neutron beam tube

P.H. Liem, H. Sekimoto / Graphite moderated helium-cooled HFR 225

(2) Vu~ can be made large enough to meet the user's need for experimental space.

(3) Accessibility to the experiment region, as con- trasted with filling the space with a solid modera- tor. Such accessibility is important in making the structural modifications that may be anticipated with a variety of experiments.

(4) Since the experimental apparatuses are separated from the core by the inner graphite reflector region and heavy water, the temperature surrounding the apparatus can be kept low so that experimental apparatuses may be designed more easily. If neces- sary the apparatuses in the heavy water region may be cooled easily through the natural convection of heavy water or with an auxiliary forced cooling system.

Since heavy water has a very low neutron absorp- tion cross section, there is no significant loss of thermal neutron attenuation as the diameter of the central heavy water region is increased to allow larger space for neutronic experiments and their support structures.

There are several functions of the inner graphite reflector. Firstly, it is needed as a structural part of the reactor and it also thermally separates the heavy water region from the core region. Secondly, the inner reflec- tor attenuates the fast neutron flux so that the optimal neutron spectral purity inside the inner experimental region may be obtained. Thirdly, the reflector provides the epithermal neutron fields needed for irradiation tubes, as shown in fig. 3.

The optimal thickness of the inner graphite reflec- tor has to be determined to achieve high values of FOMs, in particular, the maximum thermal neutron flux, thermal neutron spectral purity and usable vol- umes. We investigated the relation between th ~bma x and the core and inner graphite reflector dimensions; the result is shown in fig. 4, in terms of contour lines of

th 4~m~ as a function of the inner reflector and core width. The analysis is simplified by excluding the heavy water region. The first objective of the analysis is to obtain the optimal range of width of the inner graphite reflector, which is not strongly effected by the exis- tence of the central heavy water region. The second objective is to obtain a rough estimation of the optimal range of core geometry so that further calculations may be done only for the near optimal cases. In the analy- sis, the reactor power, core volume, and effective mul- tiplication factor kee e are fixed at 100 MWth, 10 7 c c

and 1.08, respectively. These values produce an aver- age power density of 10 W/cc . It can he observed first that the inner graphite reflector may not be too thick (over 30 cm) since the flux will be unacceptably attenu-

200

150

i "-r" I---

~oo

0 u

50

+ [./cm I "O" " 9 2 S

" . .

I I 50 100

INNER REFLECTOR WIDTH (cm)

Fig. 4.

ated. Secondly, for a fixed value of inner reflector thickness, the core thickness has a more dominant

th effect on ffma~ than does the core height. However, later it is found that the core height has a more dominant influence in increasing V,~ than does core width. Therefore, core height and width must be opti- mized in the context of acceptable flux attenuation and

["use. Naturally, with constant Q larger values of V~o =

increase ken and the fissile loading can be further diluted, therefore, higher values of neutron flux can be obtained. A more effective way to increase the thermal neutron flux is to increase the power density (el. eq. (1)), but, for gas-cooled reactors, the safety require- ment puts an upper limit on the core power density. We chose not to design an excessively high power density core since it requires an extensive development of the gas-cooled fuel element technology. Therefore, it was necessary to increase Veore to some extent, to avoid an excessively high core power density.

Lastly, the outer, top and bottom reflectors are discussed. These reflectors are needed for minimizing the neutron leakage and to provide structural strength to the whole reactor. As already stated, the core is loaded with a low fissile atomic density so that its migration area is relatively large. Thus, the core is more transparent to neutrons than conventional reac- tors and neutron leakage from the core must be con- trolled. The graphite reflectors also serve as heat sinks that are beneficial to the control of off-normal or

226 P.H. Liem, H. Sekimoto / Graphite moderated heliura-cooled HFR

Table 4 Figures of merit and controlling parameters

FOM Controlling parameters

Max. therm, neutron flux or Max. therm, neutron flux

power density

Usable volume

Spectral purity

Accessibility

fissile atomic density moderation ratio

core-reflector geometry

core volume power o r /and power density

D20 region radius (for thermal spectrum)

inner reflector (for epithermal spectrum)

core height

inner reflector width moderation ratio

(neutron spectrum) core-reflector geometry

D20 region diameter/height

accident events. This is especially true during the loss of helium forced circulation.

The above discussions are summarized in table 4, through the FOMs and the design parameters which control them.

2.2. Calculational methods and data

The DELIGHT-7 cell calculation code [2], that is based on the collision probability method, is used to prepare four group microscopic cross section sets for neutron diffusion and burn-up calculations. In the cell calculation the fast and thermal energy group struc- tures consist of 61 and 50 fine energy groups, respec- tively (total 111 fine energy groups). The energy boundary for fast and thermal energy regions is 2.38 eV. For resonance nuclides, double heterogenity of the fuel lattice is included in the calculation of the effective resonance cross section. The input nuclear data used for DELIGHT-7 code are originated from the E N D F / B - I V [3] nuclear data library; E N D F / B - I I I [4] is also used for several fission products (FPs). The carbon scattering kernel is prepared with the free gas model or theoretical kernel models.

The neutronic calculations use a four group diffu- sion method in r - z cylindrical geometry. The on-line refueling with multipass fuel cycle along with the neu- tron diffusion problem is solved to predict the fuel

bum-up or residence time, FPs accumulation and core equilibrium condition, as proposed by Y. Hirose et al. [5]. In the multipass fuel cycle, the pebble fuel ele- ments flow through the core numerous times before being finally discharged. The effective time where the pebble fuel elements reside in the core is expressed by the fuel residence time. Fuel elements with longer fuel residence time have a higher burn-up.

3. Thermal hydraulics

3.1. Thermal-hydraulic models and data

The assessment of the flow and thermal hydraulics inside the core containing pebble fuel elements are based on the combination between theoretical models and experimental /empirical data. For the flow of he- lium coolant, experimental data are needed to deter- mine the pressure loss coefficient (which usually is expressed in terms of the Reynolds number). These experimental data are then used in the momentum equation to obtain the helium flow pattern. Cross flow occurs in the pebble bed core; and flow in the trans- verse direction is calculated with the same correlation as in the vertical direction [6]. This justification is based on the randomly packed pebble fuel elements configuration in the core so that flow resistance is not orientation dependent. The flow pattern is then used to obtain the heat transfer coefficient from pebble surface to coolant which is commonly expressed in terms of Nusselt number.

Effective radial and axial heat conductivities of the pebble bed core were also determined experimentally taking into account convection, conduction, and radia- tion [7,8].

The physical model and thermal data used in the present analysis will now be presented. The equation for the mass balance of the helium coolant flow can be written as follows.

v . a = 0, (2)

where

a =pv. (3)

The pressure gradient equation consists of frictional and gravitational parts and expressed as follows.

VP = - F + pg , (4)

P.H. Liem, H. Sekimoto / Graphite moderated helium-cooled HFR

OUTER ITERATION

where

g / 1 - O G F

D 03 2p G' (5)

and

G = 161. (6)

The following pressure loss coefficient ~ was used [8].

320 6 - -+( R e / 0"1" (7) ,T=i,

The energy balance equations for the fluid and solid phases are

Vkf,°,,. Vr , - V(poC,,:rf) + ,~h(~r s - ~f) = 0, (8)

and

Vks,ef f. VT s + Q + a h ( T f - Ts) = 0, (9)

respectively, where kf, en and k~,ef f are the effective core conductivities for fluid and solid phase, respec- tively [7,8].

The pebble surface to coolant heat transfer coeffi- cient (h) is derived from the following Nusselt number correlation [8].

hD Pr 1/3 Pr 1"2 Nu = ~ = 1.27 0-~T.18 Re°'36 + 0.033 0--d~.07 Re°'86

(10)

And last, the conservation law of energy in the solid phase yields the equation for the temperature in the pebble,

Vkp. VTp + Qp = 0. (11)

The conductivity of graphite under neutron irradiation decreases significantly, and the degraded graphite con- ductivity (kp) must be used to obtain accurate pebble center temperature [9]. In the calculation, the de- graded kp is calculated by taking account the fuel burn-up and pebble temperature.

Next, the appropriate boundary conditions are dis- cussed. For the mass and momentum balance equa- tions (eqs. (2) and (4)), the inlet condition, i.e., total mass flow and inlet pressure are given as the boundary conditions. For the solid and fluid phase energy bal- ance equations (eqs. (8) and (9)), the inlet coolant and pebble surface temperatures are given. Although a small part of the fission energy generated inside the

GIVEN CORE GEOMETRY

FUEL ELEMENT GEOMETRY POWER DENSITY DISTRIBUTION

1. CALCULATION

MOMENTUM BALANCE CALCULATION

1. I FLUID PHASE ENERGY

BALANCE CALCULATION

1 I SOLID PHASE ENERGY

BALANCE CALCULATION

PEBBLE INNER [ TEMPERATURE CALCULATION

Fig. 5.

INNER ITERATION 1

227

INNER ITERATION 2

core is transferred into the reflector regions, here, we take a conservative boundary condition, i.e., the adia- batic boundary condition at both the inner and outer radial boundaries of the core, as well as at the bottom of the core. The boundary condition for the conduction problem inside the pebble fuel element (eq. (11)) is the pebble surface temperature.

The coupled non-linear mass, momentum and en- ergy balance equations must be solved to obtain fuel temperature distribution and pressure drop across the core. The overall numerical procedure is depicted in fig. 5. Intuitively, the mass and momentum balance equations pair and similarly the fluid and solid energy balance equations pair are tightly coupled, so that an inner iteration loop for each pair is provided. An outer iteration loop connects the two pairs of balance equa- tions. When the iterative procedure has converged, the helium flow and temperature distributions, pebble sur- face temperature and core pressure drop are obtained and the conduction equation for the pebble fuel ele- ment can be readily solved.

228 P.H. Liem, 1-1. Sekimoto / Graphite moderated helium-cooled HFR

Taking into account the axisymmetry of the reactor geometry, the above equations are formulated in a r -z geometry. A finite difference method is used in most of the numerical calculations.

3. 2. Design objectives and procedures

As shown in table 1, the objective of the thermal-hy- draulic design is to minimize the steady-state fuel oper- ating temperature as low as possible. From safety point of view, the objective is important in that the HFR has to be protected from off-normal or accident events, which may include a loss of forced circulation (LOFC) with or without depressurization accident. No com- plete discussion of the safety and accident analyses is given here since it will be presented in other papers. It is worthily emphasized here that the initial low fuel temperature is not the only factor which determines the HFR safety during the off-normal and accident events. However, a low initial fuel temperature prior to the accidents is obviously advantageous.

In the present design, the fuel limit temperature is taken conservatively to be 1,600"C [10]. Large margins between the operating maximum fuel center tempera- ture (Tp,m~) and the fuel limit temperature are desir- able, which can be achieved by combination of the following effects: (1) Lowering the coolant inlet temperature (Ti,) and

decreasing the core temperature rise (AT = Tou t -

Ti.). (2) Higher values of system pressure (Pi.) are prefer-

able since they provide smaller core pressure drops and increased heat transfer.

As indicated in table 1, the thermal design con- straints consist of minimum inlet temperature and max- imum system pressure. In the present design the coolant inlet temperature is limited to be higher than 200"C to avoid problems concerning the Wigner effect. Decreas- ing the core temperature rise means increasing the coolant flow which is expected to enhance the heat transfer in the core. A coolant flow increase produces a higher core pressure drop, and in turn demands a larger pumping power. The HFR design demands no advanced technology of the gas-cooled reactor contain- ment/pressure vessel so that the maximum system pressure is constrained to be less than 5 MPa.

To understand the effectiveness of the above effects in lowering the maximum fuel center temperature, we give an approximate analytical expression of Tp,ma ~. As discussed in the Appendix, Tp,m~ consists of summa- tion of the coolant temperature (Tf), fluid-pebble sur- face temperature increase (ATfs), and pebble surface-

center temperature increase (ATsc), which are evalu- ated at the location of the maximum temperature.

Tp,m~ , = Tf + aTf, + ATe. (12)

The first term T e increases linearly with AT. Hence, a decrease of the coolant inlet temperature and core temperature rise (AT) results in a proportional de- crease of Tf, which contributes in lowering the Tp,m~ ,. For constant Q and D, the second term AT~s which is expressed approximately by eq. (A-14) depends strongly on AT 0"86. The last term /tT,~ depends only on 1/kp, and increases as kp decreases as the temperature increases. These two terms also decrease as the core temperature rise (AT) decreases.

As the core temperature rise decreases (or the coolant flow increases), the core pressure drop behav- ior may be approximately given by eq. (A-7), rewritten below.

Q /19{ 1 / 1"1 A p ~ ( - ~ ] -~1 (Tin+AT/2) 1"07. ( 1 3 )

For constant Q and D, it is obvious that lowering the Tou t by increasing the total coolant flow will increase the AP almost quadratically.

4. Analysis results

Using the design procedures discussed above, sev- eral neutronic and thermal calculations were done to search optimal ranges of various design parameters which give high values of FOMs and to meet the thermal design objective. The neutronic calculation result shown in fig. 6 gives the optimal ranges of core

t , i ' i ' i ' i i .

I " , . S th(D 20)(x 100) , , , 2r- \ Vu° c/ I--

• I ="' ' \ v~o)'5~'---.~ (xlts)

- " ~ s , . ( c l ( x l o )

(1015crn-2s -1) CORE , ,

WIDTH 40 6~0 80 iota) RESID. t I t TIME 114 31 33 (day)

Fig. 6.

P.H. Liera, H. Sekimoto / Graphite moderated helium-cooled HFR 229

Table 5 Neutronic and thermal design parameters

Geometry Heavy water radius 50 em Inner reflector radius (Wrt) 30 em Core inner radius 80 cm Core volume (Vcore) 107 cc Outer, top, bottom refl. width 200 era

Thermal Power (P) 150 MW Ave. power density (Q) 15 W/cc Core void fraction (0) 0.39 Coolant inlet temperature (Tt,) 200"C System pressure (Pi,) 5 MPa

geometry (i.e., the core height and width) in which high values of FOMs are achieved and the maximum ther- mal neutron flux is in the vicinity of 1015 em -2 s -1. To achieve such a high thermal neutron flux, the neutronic and thermal design parameters shown in table 5 are used.

A discussion of the selected parameters, shown in the table, is given. The heavy water region diameter is taken to be 100 cm which is considered large enough for various neutronic experiments. As already dis- cussed, the inner graphite reflector thickness is optimal around 30 cm. The fresh fuel 235U'smear density is 3 × 101S/ce. In the calculation, the core volume and power density are fixed at 107e¢ and 15 W/ec , respec- tively. We are not encouraged to increase the power density further, since it will demand a new high tem- perature gas reactor fuel technology. Using the above values, the reactor power is readily obtained, i.e., P = 150 MWth. From preliminary calculations it was found that outer reflector thiekneiss of 200 cm was acceptable in controlling neutron leakages. The selection of ther- mal design parameters, which include system pressure and inlet temperature, are already given in the ther- mal-hydraulic sections.

In the figure, the optimal range of the core width is from 40 and 90 era (core heights from 398 to 141 cm). Outside this range, the th 4~max decreases significantly. The FOMs for usable volume, Fuse, and thermal neu- tron spectral purity, S th, are broken down into two element, each for the central heavy water and inner graphite reflector regions. The FOM for ~mm~/Q is not drawn but easily obtained by dividing the value of d'maxth with the average power density Q = 15 W/cc .

Some conclusions may be drawn from fig. 6. For a core width range from 40 to 90 cm the FOMs values for the thermal spectral purity and maximum thermal

,p oo,

t RE WIDTH=50 cm " ~%1 I--" ot lo

100 260 360 ' lJ' Tout-Tin(C)

Fig. 7.

neutron flux do not vary significantly. T h e thermal spectral purity for the central heavy water region is higher by over than one order of magnitude than that for the inner graphite reflector region. This indicates that the fast neutron component in the graphite reflec- tor region is higher and epithermal neutron irradiation experiments may be conducted in that region. The core height has a significant effect on Fu~. We further

I (1014 ¢rn-2s -I)

top refl.

- J / s " ~ / 441 I 50 80 140 I

(:~)

Fig. 8.

----~r(cm)

230 P.H. Liem, H. Sekimoto / Graphite moderated helium-cooled HFR

evaluated the accessibility of the central heavy water region from its geometrical point of view, i.e., the ratio between diameter and height of the region (D/H) . This accessibility FOM becomes worse for the smaller ( D / H ) associated with slender core.

The fuel residence time, as one result of the bum-up calculations, decreases significantly for a slender annu- lus core. The slender cores quickly lose their criticality condition, and fresh fuel has to be added at increased rates. Of course this demands a larger reserve fuel inventory.

In die optimal range of core geometry, the values of S th (both for heavy water and inner graphite reflector regions) and m Om~ are essentially independent of the core geometry. However, V ~ and its accessibility show reverse behaviors. Thus, the core geometry has to be optimized to obtain acceptable Vu~ and its accessibil- ity, when the user's or experimenter's need are made clear, Those needs are not yet defined, but when defined, the HFR design can be evaluated quite well through the FOM graphs in fig. 6.

The thermal-hydraulic calculation result is shown in fig. 7. In the figure, ziP and Tp,m~ , are drawn for three values of core width in the range shown in fig. 6. Decreasing the core temperature rise (AT) will in-

r

I

z (cm)

r ( ~ )

z = 2 0 0

z=441

Fig. 10.

I I

z (cm)

50 80 140

Fig. 9.

cm) crease the core pressure drop, but decrease the maxi- mum fuel center temperature. Smaller core width or larger core height gives a significantly larger pressure drop, but, the maximum fuel temperature is not strongly affected by the core dimension change. It can be ob- served from the figure, Tp,m~ x is almost linearly propor- tional with AT. If a value of the maximum core pres- sure drop APm~ , is chosen, we may estimate the maxi- mum fuel center temperature from the figure and obtain the safety margin of the design.

Here, a representative standard case is chosen, in which the core width and height are 60 and 241 cm, respectively, and the core temperature rise is 100°C. For this standard case, the core dimension gives the highest value of maximum thermal neutron flux. The neutronic calculation results, i.e., the thermal neutron flux and the ratio of thermal to fast neutron flux distributions are shown in figs. 8 and 9, respectively. The maximum thermal neutron flux is located in the heavy water region at 5 cm from the inner graphite reflector surface. The usable volume is denoted by the shaded area. The thermal to fast neutron flux ratio does not change significantly in the axial direction, but in radial direction. The map of the ratio which shows the degree of thermal neutron spectrum softness pro-

P.H. Liem, H. Sekimoto / Graphite moderated helium-cooled HFR 231

r------- r (¢m) I CORE z=200

z (cm) 260

28o~

300 , , , \ 320

\ \ 340 * C

J360 z=441

Fig. 11. Pebble fuel center temperature distribution (standard case; core width and height are 60 and 241 era, respectively).

For one standard case, a maximum thermal neutron flux of more than 1.0 × 10 is cm -2 s - j , with thermal neutron spectral purity of more than two orders of magnitude and usable volume of more than 1,000 liters can be obtained in the central heavy water region, for a reactor power and core volume of 150 MWth and 107 cc, respectively. In the inner graphite reflector, the same level of thermal neutron flux with ephithermal spectrum and a usable vlume of 1,800 liters can be obtained.

The thermal-hydraulic design objective is to provide a large temperature margin between the maximum fuel center temperature and fuel limit temperature. A low initial fuel temperature is advantageous in protecting the HFR during off-normal and accident events. For the standard case, the design provides a maximum fuel center temperature lower than 400"C, which provides a safety margin of more than 1,200°C prior to the acci- dent.

The final design of the HFR may be completed when specific requirements and specifications of the neutronic experiments a n d / o r their aparatuses are provided.

The primary HFR design concept, i.e., (1) diluting the fissile loading in the core, and (2) optimizing the core-reflector geometry, to maximize the thermal neu- tron flux was proven effective. Future work will include safety analysis and accident simulation.

vides a valuable information for further detail plan of the experimental apparatuses and their locations.

The power density and pebble center temperature distributions are shown in figs. 10 and 11. The multi- pass refueling scheme adopted for this design limits the variation in power density distribution as shown in fig. 10. The maximum power density is located in the middle of the core. The Tp,ma x is located near the bottom of the core, as illustrated in fig. 11.

Acknowledgment

The authors express their gratitude to Dr. M. Ari- tomi of Tokyo Institute of Technology for his advice in performing the thermal analysis, and to Mr. K. Ya- mashita of Japan Atomic Energy Research Institute for his advices in using the DELIGHT-7 code system.

5. Conclusion

Neutronic and thermal-hydraulic design procedures for the graphite moderated gas-cooled high flux reac- tor were presented. The neutronic design objective is to achieve high values of FOMs. The H F R design with high values of FOMs can provide a high maximum thermal neutron flux with an optimal thermal neutron spectral purity and a large usable volume for various neutronic experiments. In this work, the result of the design was presented as the optimal ranges of several design parameters which give high values of FOMs.

Appendix

Firstly, a detail derivation of the core pressure drop is given. With fixed core geometry, the coolant mass flux, G, may be expressed as:

Got Q / AT . ( A - l )

The correlation for the pressure loss coefficient qt in the turbulence flow regime may be approximated as,

6 = (A-2)

( R e / ( 1 - 0) ) 0.2,

232 P.H. Liem, It. Sekimoto / Graphite moderated helium-cooled HFR

with the following definition of Reynolds number,

Re ffi GD/I~. (A-3)

Also, the coolant thermal properties, i.e., the coolant mass density and viscosity dependency on the tempera- ture can be written as (the physical properties are evaluated for the average coolant temperature),

1 P ot Tin + AT~2' (A-4)

and

ot (Tin + AT/2) °'6s7, (A-5)

respectively. By neglecting the gravitational effect, the pressure

drop equation eq. (4) may be formulated as,

qt 1 - 0 IGI VP= D 0 3 2p G. (A-6)

Using the above relations, the dependency of pressure drop across the core on thermal properties and param- eters may be expressed as:

( Q /19[ 1 / 1"1 APOt~-'~j !,'-D} (Tin+AT/2)l'°7" (A-7)

Secondly, the maximum fuel temperature is derived. The maximum fuel center temperature may be ex- pressed as:

Tp,ma x = rf + aTfs + ATse. (A-8)

With no severe power peaking, the maximum fuel center temperature will be located near the outlet (or bottom part) of the core, so we can conservatively take Tf as Tout,

Tfot Tin + AT. (A-9)

The dependency of ATsc on pebble diameter and con- ductivity is:

ATsc ot ( QDE/kp ). (A-10)

Similarly, the dependency of AT~ is:

ATts ot (QD/h ). (A-11)

Approximating the Nusselt number for large Reynolds number (turbulence flow regime), the heat transfer coefficient dependency may be written as,

( k f ) / 1 /0"14[ Q / 0.86 hot ~ ~-~] - ~ ] (Tin+aT) . (A-12)

Using the coolant conductivity dependency on temper- ature,

kf ot (Tin + AT) 0"701. (A-13)

together with the relations obtained for the mass den- sity and viscosity, the relation for fluid-pebble surface temperature increase may be formulated as:

ATf~ ot DI'14Q°'14AT°'S6"(Tin + AT) -0.1. (A-14)

Nomenclature

A c~ Cp D E f g G h H kf kf,eff kp ks,elf k® MR N, Nu P P Pr Q r Re S th

Tf

T~

Vcore V ~ Wc WR Ap AT AT~ AT~

accessibility of usable volume, energy per fission for nucleid i, coolant heat capacity, pebble diameter, neutron energy, thermal utilization factor, gravitational acceleration, coolant mass flux, coolant heat transfer coefficient, core height, helium conductivity, fluid phase core effective conductivity, pebble conductivity, solid phase core effective conductivity, infinite (cell) multiplication factor, moderation ratio, atomic density of nucleid i, Nusselt number, resonance escape probability factor, reactor thermal power, Prandtl number, power density, position, Reynolds number, thermal neutron spectral purity, coolant temperature, pebble surface temperature, pebble inner temperature, coolant mass velocity core volume, usable volume, core thickness, inner graphite reflector width, core pressure drop, inlet-outlet coolant temperature difference, coolant-pebble surface temperature increase, pebble surface-center temperature increase, pebble surface to volume ratio, neutron flux,

P.H. Liem, H. Sekimoto / Graphite moderated helium-cooled HFR 233

P

0

fast fission gain, no. of neutrons produced per neutron ab- sorbed, coolant viscosity, pressure loss coefficient, coolant mass density, microscopic fission cross section for nuclied i, core void fraction.

References

[1] P.H. Liem, H. Sekimoto and E. Snetomi, Nucl. Instr. and Meth. A274 (1989) 579-583.

[2] R. Shindo, K. Yamashita, I. Murata, DELIGHT-7 - one dimensional fuel cell burnup analysis code for High Tem- perature Gas-cooled Reactors (HTGR), JAERI-M 90-048 (March 1990).

[3] D. Garber, ENDF/B Summary Documentation, BNL- NCS-17541 (ENDF-201), 2-nd Edition (1975).

[4] D. Garber, ENDF/B Summary Documentation, BNL- NCS-17541 (ENDF-201), 1-st Edition (1975).

[5] Y. Hirose, P.H. Liem, E. Suetomi, T. Obara and H. Sekimoto, J. Nul. Sci. Tecimol. 26 (1989) 647-679.

[6] G. Melese and R. Katz, Thermal and flow design of helium-cooled reactors (American Nuclear Society, Illi- nois, 1984) pp. 145-146.

[7] D.R. Vondy, PEBBLE - a two-dimensional steady-state pebble-bed-reactor thermal-hydraulics code, ORNL-5698 (September 1981).

[8] K. Verfondern, Numerical investigation of the 3-dimen- sional steady-state temperature- and flow distribution in the core of a pebble bed high temperature reactor, Jiii-1826 (January 1983).

[9] L. Binkele, Ein Verfahren zur Bestimmung der W/irmeleitfiihigkeit yon neutronenbestrahlten Graphiten bei Temperaturen zwischen 50 nnd 1000°C, Jiil-1096-RW (August 1974).

[10] K. Verfondern, W. Schenk and H. Nabielek, Nucl. Tech- nol. 91 (1989) 235-246.