JAERI-Data/Code 94-013

JAEUI-Data/Code—94-01

JP94112A8

VHTRC TEMPERATURE COEFFICIENT BENCHMARK PROBLEM

October 1 9 9 4

Hideshi YASl'DA, Tsuyoshi VAMANF and Toshinobu SASA

Japan Atomic Energy Research Institute

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This reporl is issued irtvgularK

Inquirifs ahoiil a\;iihibilit> ol the reports should he addressed to Information Division.

Department of Technical Information. Japan Atomic Fneri>\ Research Institute. Tokai-

mura. \aka-gun. Ibaraki-ken .'14-11. Japan

II ¥%i i I] W 'it "«i

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• I A K N I I i . i i , - i r . , , i , - i n u i : t

VHTRC Temperature Coefficient Benchmark Problem

Hideshi YASUDA, Tsuyoshi YAMANE and Toshinobu SASA

Department of Reactor Engineering

Tokai Research Establishment

Japan Atomic Energy Research Institute

Tokai-mura, Naka-gun, Ibaraki-ken

(Received September 13, 1994)

As an activity of IAEA Coordinated Research Programme, a benchmark problem

is proposed for verifications of neutronic calculation codes for a low enriched uranium

fuel high temperature gas-cooled reactor. Two problems are given on the base of

heating experiments at the VHTRC which is a pin-in-block type core critical assembly

loaded mainly with 4 % enriched uranium coated particle fuel. One problem, VH1-

HP, asks to calculate temperature coefficient of reactivity from the subcritical

reactivity values at five temperature steps between an room temperature where the

assembly is nearly at critical state and 200 °C. The other problem, VH1-HC, asks

to calculate the effective multiplication factor of nearly critical loading cores at the

room temperature and 200 °C. Both problems further ask to calculate cell parameters

such as migration area and spectral indices. Experimental results corresponding to

main calculation items are also listed for comparison.

Keywords. Benchmark, Calculation, Temperature Coefficient, VHTRC, Low Enrich,

HTGR, Multiplication Facto1". Experimental Value, IAEA

• . \ l - I I v 1 l i . ' i i ' " ' l r ' J ! i l l : ' .

VHTRC filf f&Bt^ •;

(1994 ip 9 13 ESS?)

'^tL® (CRP)

BiaS^m* L fco C nnmtt £'><< y?a-,9 mP,^ t oiOfjg *" X^SSs^^^^iS VHTRC

^ 200 °C * X'<F> 5 ©PS^gAfSx r v 7°tcJ>f L t .

VHl-HC rn1S@r-|i^ffl&t>' 200 "C T l i lJE i l^ lc^S <£ T IC'KW^^a^lSPS L fcttffi

ー¥

VHTHC温度係数ベンチマーク問照

日本原子力研究所東海研究所原子炉工学部

安田秀志・山根 岡IJ・佐々敏信

11994年 9月13日受理)

低濃縮ウランを燃料とする高温ガス炉の炉物珂ノfラメータを核計算コードで計算する場代の精

度を検討評価する子段とするため. IAI;:八協力研究計画 (CRP)の活動の一環としてベンチマー

ク問題を作成したc この間監はピンインプロソク型炉心をもっ高副カス炉臨界実験装置VHTHC

にj二として .1%濃縮ウラン被覆粒子燃料を装荷して実施した炉心界湖実験に基づいて作成したっ

VH1-IlP問題では.ほほ臨界状態となる首1・t品から 200T までの 5段階の温度ステソプに対して.

それぞれの臨界未満度から制度ステゾプ聞の反応度制度係数を算出することを求めており.

VHl-lIC問題アは常温及び 2000

Cでほほ臨界になるように燃料装荷量を調節した状態での集fT

f本の'J~".7Jt自供係数を算出することを求めているしr-.ðC両問題ではさらに.移動面積. スベクトル

指標等のセル計算の結果を出すことも求めているつ比較に供するため.主な計算結果に対応する

実験結県も示した。

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11

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Contents

1. Introduction 1

2. Benchmark Name and Type 1

3. System and Experiment Descriptions 1

4. Model Description 2

4.1 Assembly 2

4.2 Fuel Rod 2

4.3 Boundary Conditions 3

4.4 Neutron Energy Groups 3

4.5 Assembly Temperature 4

4.6 Effect of Thermal Expansion of Assembly 4

4.7 Loading Irregularities 4

5. Requested Calculation Results 4

6. Experimental Results and Others 5

Acknowledgement 6

References 6

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Contents

1. Introd uction ・H ・-

2. Benchmark Name and Type

3目 System and Experiment Descriptions '"

4目 ModelDescription …...・ H ・.....・ H ・..…...・ H ・......…...・ H ・..…....・ H ・.....・ H ・.....・ H ・....・ H ・ 2

4.1 Assem bly ..…'"・ H ・..…...・ H ・..…...・ H ・........・ H ・....・...…・・…...・ H ・.....・ H ・.....・ H ・..…・・ 2

4.2 Fuel Rod .......・ H ・.....・ H ・..…...・ H ・.....・ H ・..…'"・ H ・.....・ H ・.....・ H ・.....・ H ・....・ H ・...・ H ・ 2

4.3 Bound斗ryConditions ・H ・.....・ H ・H ・H ・..…...・ H ・-…………...・H ・H ・H ・..…...・ H ・..…・ 3

4.4 Neutron Energy Groups ・・・・・・・・・・・・・・ H ・H ・.......................・ H ・......・ H ・.........・・・・・・....・・ 3

4.5 Assem bly Tem perature ・H ・..…............…・・ H ・H ・'"・・……...・ H ・......・ H ・.....・ H ・ 4

4.6 Effect of Thermal Expansion of Assembly …・・・・ H ・H ・……...・ H ・.....・ H ・..… 4

4.7 Loading Irregularities ……...・ H ・H ・H ・"…...・ H ・.....・...………...・ H ・・ H ・H ・.....… H ・H ・ 4

5. Requested Calculation Results …...・ H ・"…...・ H ・..…・…・……… H ・・ H ・H ・.....・ H ・.....・ H ・ 4

6. Experimental Results and Others ・H ・H ・H ・.....・ H ・...…...・ H ・H ・…・....・ H ・......・H ・ 5

Acknowledgement ・・ H ・H ・.....・ H ・.....・ H ・.....・ H ・......・ H ・H ・H ・-……...・ H ・H ・H ・..…..，・ H ・......・ H ・ 6

References ...・ H ・..…..…...・ H ・.....・ H ・.....・ H ・.....・ H ・.....・ H ・.....…………...・ H ・..…...・ H ・.....・ H ・ 6

目 次

l はじめに

2. ベンチマークの名前と形式

3目 システムと実験の説明

4. モデルの説明 ...・ H ・..…...・ H ・.....・ H ・一… H ・H ・......・H ・.....・ H ・...・ H ・H ・H ・.，....・ H ・............. 2

4.1 集 合 体 ...・ H ・..…....・ H ・....・ H ・-……・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 2

4.2 燃 料 棒 ....・ H ・-…....・ H ・-…・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 2

4.3 境界条件………….....・ H ・.....・ H ・.....・ H ・.........…・...・ H ・.......・ H ・...・ H ・...・ H ・..… H ・H ・ 3

4目4 中性子エネルギ一群…...・ H ・..…...・ H ・..…...・ H ・.....・ H ・.....・ H ・.....・ H ・........・ H ・..…・・・… 3

4.5 集合体の温度...・ H ・.....・ H ・.....・ H ・..…...・ H ・.....・ H ・..…....・ H ・.....・ H ・.....・ H ・.....・ H ・H ・H ・ 4

4.6 集合体の熱膨張の効果...・ H ・...・ H ・....・ H ・....・ H ・....…...・ H ・H ・H ・.....・ H ・...・ H ・.....・ H ・...… 4

4.7 装荷の不規則性 …・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 4

5. 要求される計算結果 ・・ H ・H ・...・H ・.......・ H ・...・ H ・...・ H ・....…….....・ H ・.....・ H ・...・ H ・....・ H ・-… 4

6. 実験結果その他 ..，・ H ・......・ H ・..……………...・ H ・.....・ H ・-…...・ H ・-… H ・H ・-… H ・H ・.....・ H ・ 5

謝 辞 …・・・H ・H ・...・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 6

参考文献 ....・H ・-…・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 6

111

-i \ i - : m D . i . i ( • , „ ] , >n n; .1 .

1. Introduction

A benchmark problem is presented for verifications of neutronic calculation codes

for a low enriched uranium fueled HTGR on the basis of heating experiments at a Very

High Temperature Reactor Critical (VHTRC [1] ) Assembly

This benchmark should be useful for verifying,

(1 )Evaluated nuclear data for low enriched uranium-graphite systems

(2)CalcuIation of effective multiplication factor for different temperatures which yields

temperature coefficient through cell and whole reactor calculations

The calculated multiplication factor can be compared with experimental values listed

in tables of this paper.

This benchmark problem was originally distributed only to institutions participating

in the IAEA Coordinated Research Programme(CRP) on "Validation of Safety Related

Reactor Physics Calculations for Low-Enriched HTGRs". This document aims to open

the problem tc the public.

2. Benchmark Name and Type

Benchmark Name:(I) VH1-HP

:(2)VH1-HC

Type: (1) VH1-HP asks to determine the temperature coefficient of reactivity for five

temperature steps. [2]

: (2) VH1-HC asks to determine the effective multiplication factor of two nearly

critical cores at two temperatures.[3]

3. System and Experiment Descriptions

The VHTRC is a graphite moderated critical assembly which has a core loaded with

pin-in-block fuel of low enriched uranium and a graphite reflector. A bird's eye view of

the assembly is shown in Fig. I. The assembly has a hexagonal prism shape The surface

of the assembly is covered with 0.5 mm thick Cd sheets as thermal neutron absorber and

10 or 15 cm thick Alumina-Silica fiber blankets as heat insulator. The assembly consists

of two axially-jointed hexagonal-prism half assemblies. The structure of the half

assemblies are made of graphite blocks supported with steel frames as shown in Fig. 2.

A cross section of a graphite block (fuel block) is shown in Fig 3.

Fuel rods are inserted in holes of the graphite blocks of each half assembly, each rod

1 -

.1 \ K K 1 1 1 : , ! , , c . . , i . ' H n | • ;

being paired with a solid graphite rod to make axial length, 120 cm One fuel rod

consists of 20 fuel compacts, one graphite sheath and two graphite end caps as shown in

Fig. 4. The shape of fuel compact is hollow cylinder. The fuel compact is made of

coated fuel particles uniformly dispersed in graphite matrix. The coated fuel particle is,

so called, BISO-type which has two carbon layers on uranium dioxide kernel The cross

section of a coated fuel particle is shown in Fig. 5 There are two types of fuel compacts.

B-2 and B-4 which differ essentially in the uranium enrichment By using separately the

two types of fuel compacts, two types of fuel rods, B-2 and B-4 rods, are prepared for

the experiments.

The assembly was heated from a room temperature up to 200 "C by using cartridge

type electric heaters inserted axiaily in the radial reflector At the room temperature, the

assembly was critical in experiments corresponding to both VH1-HP and VH1-HC

problems. In the course of assembly heating, the assembly temperature was kept

constant and isothermal condition was realized at several steps of assembly temperature

Subcritical reactivity was measured by pulsed neutron method in the experiment

corresponding to VH1-HP, on the other hand, critical point was measured by fuel md

addition and control rod adjustment in the experiment corresponding to the second step

of VHI-HC.

4. Model Description

4.1 Assembly Assembly dimensions are given in Table 1 The core is loaded with fuel rods in the

pattern shown in Fi«. 6 for both all steps of VH1-HP and the first step of VHI-HC.

while for the second step of VHI-HC, the core is loaded in the pattern shown in Fitz_7.

The movable and fixed half assemblies are loaded with fuel rods symmetrically In the

whole reactor calculation, the configurations can be well dealt by a three dimensional

T(Triangular)-Z model considering the symmetry. However, It can be reduced to a

simplified two-dimensional R-Z model by keeping cross sectional area as shown in Fiu

8(a} In the R-Z model, calculation will give about 0 1 °b lower values of kcif for VH1-

HP and 0.2 % higher values for VHI-HC(200tr) than those by the T-Z model These

evaluations are obtained through the cell calculation by collision probability method and

the whole reactor calculation by diffusion theory using SRAC[4] code with an ENDF7B-

IV based nuclear data library.

4.2 Fuel Rod A cross section of a fuel rod should be modelled as shown in Fiu 4 In this model.

. 1 \ l - . l ; | I M : i i ' . . . I . > i e l . - :

one end cap on the core mid-piane side is homogenized with fuel region of fuel compact

and the other end cap is treated as a part of the axial reflector

In the cell calculation, one fuel block can be modelled as a unit cell as shown in Fjg_

9. Dimensions of a fuel block are shown in Table 2 On the other hand, one fuel rod

with surrounding graphite (one twelfth of a graphite block) can also be modelled as a

unit cell as shown in Fig. 8(b). There should be no difference, in principle, between

results by the two models, it should be noted that the pitches between fuel rods in a

graphite block have a common value, however, they are not equal to the distance

between two adjacent fuel rods in neighboring two graphite blocks. The two kinds of

heterogeneity, i.e., rod-wise and particle-wise, should be taken into account The

particle-wise heterogeneity can be modelled as shown in Fig. 8(c). If the rod-wise

heterogeneity is considered and tlie particle-wise heterogeneity is neglected, the result

will give about 0.8 % lower value for kcjj. This difference was also estimated by the

SR.AC Dimensions of a graphite sheath and an end cap are listed in Table 3 In Table

4, are shown dimensions and uranium content of a fuel compact. Isotopic abundance of

uranium in a fuel kernel is listed in Table 5. In Tab|e_6, are listed the detail of calculated

atom densities in the fuel compact. The atom densities of the fuel compact homogenized

over particles, matrix graphite and an end cap on the core mid-plane are shown in Table

7. The end cap homogenization effect is estimated to be neglibibly small on ke/j;

Average number of coated fuel particles in a fuel compact is given in Table 8. Atom

densities for graphite assembly and sheath are listed in Table 9. The number of fuel rods

in the core is summarized in Table 10.

4.3 Boundary Conditions In the cell calculation, if a cylindrical or spherical model is employed, the boundary

condition should be isotropic reflective, on the other hand, if a hexagonal model is

employed, it can be perfectly reflective. In the whole reactor calculation, a vacuum

boundary condition should be used at the surface of reflector The steel frames

surrounding the reflector have the effective thicknesses of about 2 cm in the radial

direction and 0.4 cm in the axial direction This effect was estimated to about +0.2 % in

keff and was corrected to the experimental results Therefore, the benchmark calculation

can avoid taking account of this effect.

4.4 Neutron Energy Groups Number of neutron energy groups is not specified in this benchmark calculation

Thermal cut-off energy should be 0.625 eV to calculate spectral indices

-! M . ! , 1 , ! ' r •. i ••:• ' ' I " I :

4.5 Assembly Temperature The experimental temperatures are also shown in Table 10. All the materials in the

assembly can be considered to have a common temperature at each step

4.6 Effect of Thermal Expansion of Assembly The thermal expansion effect was estimated from the change of calculated A(.//

values due to the change of assembly dimension and atomic number density between 300

and 500 K. using the linear thermal expansion coefficient of the assembly The resultant

temperature coefficient due to thermal expansion of the assembly was -1.0x10° Ak/k/iT

This etTect was subtracted from the experimental value of temperature coefficient of

reactivity Therefore, it should be neglected in the benchmark calculations

4.7 Loading Irregularities As seen in Fig 10, there are various structural irregularities in the actual assembly,

for example, safety rod insertion holes, heaters, thermocouples, partially inserted control

rods, neutron detectors, small gap between two half assemblies The reactivity effects of

such irregularities were independently measured and were excluded from the

experimental results. Therefore, in the benchmark calculations, these irregularities

should be replaced with graphite, for simplicity.

5. Requested Calculation Results

(1) Unit Cell Results

1) k.. (0), i.e., productions/absorptions for buckling B2 = 0.

2) The critical buckling B2cn, and k.K {B-c,-n), i.e., productions / absorptions for

B2 = B-cnl .

3) The migration area M- = [k... (B2crn ) - 1 ] / B2

cn( .

4) Reaction rate breakdown for the B- = B~m, case in terms of missions, captures

and productions for each nuclide with normalization to a total absorption

(fissions+ captures) of unity

5) The spectral indices p 28, d 25 , cS 28 and ('* for the B2 = B2m, case.

The spectral indices should correspond to a thermal cut-off energy of 0.625 eV and

are defined as:

p -8 = ratio of epithermal-to-thermal 2?XU captures,

(5 25 = ratio of epithermal-to-thermal 2-°U fissions.

5 28 - ratio of 2™U fissions to ^ U fissions(macroscopic),

('* = ratio 2:?XU captures to 2^"'U fissions(macroscopic)

\KI

Items 1) to 3) are to be computed for every step of temperature.

Items 4) and 5) are to be computed for the first and the fifth steps of VHl-HP and for

the second step of VHl-HC

(2) Whole Reactor Calculations

1) keff for the specified configurations and atom densities.

2) Reaction rate breakdown at the center of the core (center of the central graphite

block in the radial cross section) in terms of fissions, captures and productions for

each nuclide with normalization to a total absorption(fissions + captures) of unity,

using the effective cross section obtained by the cell calculation.

3) The spectral indices p -%, 6^ , <?28 ancj (•* usjng neutron flux at the center of the

core axis and effective cross section obtained by the cell calculation

4) Neutron balance in terms of absorption(unity), productions and leakage,

integrated over the core region.

5) 2-1sU and 238U fission rate spatial distributions along the centra! axis of core and

along the horizontal line on the axially mid-plane

6) Temperature coefficient of reactivity between the initial and final steps of VHl-HP.

In this calculation, the following definition should be used,

L_ *5(7':W£_V7'i) T2-~F\ "ic^n) k&(T\)

where a r is a temperature coefficient of reactivity. Ti , Ti denote assembly

temperatures.

7) Effective delayed neutron fraction and neutron generation time

for two steps of VHl-HC.

Item I) is to be computed for every step of temperature.

Items 2) and 5) are to be computed for the first and the fifth steps of VHl-HP and forthe

second step of VHl-HC Table 11 summarises the requested calculation items.

6. Experimental Results and Others

Experimental results of keff are shown in Table 12 Temperature coefficients of

reactivity derived from the Ae^and temperature values in the Table 12, are given in Table

]}_. The values in these tables are modified from the raw data to meet the simplification

for the benchmark. In Table 14 are given the constants which can be used in the

benchmark calculation

• l A K h ' l D . l l . i C , , , i r

A cknowledgement

The authors are indebted to Dr. K. Tsuchihashi and Dr. F.Akino for their valuable

comments and advices in the preparation of this document

References

[1] Yasuda, H., et al.: "Construction of VHTRC(Very High Temperature Reactor Critical

Assembly)", JAERI 1305, August, 1987 (In Japanese)

[2] Yamane, T, et al. "Measurement of Overall Temperature Coefficient of Reactivity

of VHTRC-1 Core by Pulsed Neutron Method", J. Nucl. Sci. Technol., Vol. 27, No

2, pi22, 1990

[3] Yasuda, H., et al: "Measurement of Temperature Coefficient of Reactivity of

VHTRC-1 Core by Criticality Method", Proc. IAEA Specialist Meeting on

Uncertainties in Physics Calculations for Gas-Cooled Reactor Cores, 9-11 May,

1990, Villigen, Switzerland, 622-I3-SP- 389.27

[4] Tsuchihashi, K. et al, "Revised SRAC Code System", JAERI 1302, 1986

- 6

\H ; I

Table 1 Dimensions of the assembly

Across flats 2400 mm

Axial length 2400 mm

Table 2 Dimensions of fuel block

Across flats 300 mm

Axial length 1200 mm

Fuel rod hole diameter 47.2 mm

Fuel rod hole pitch 65 mm

Table 3 Dimensions of graphite sheath and end cap

Graphite

sheath

Outer diameter

Inner diameter

Length

46 8

36.5

732

mm

mm

mm

End cap Diameter

Thickness

36.6 mm

5 mm

Table 4

Type

Kernel

Dimensions and

Diameter

uranium content

B-2

602 ,u

of fuel

m

compact

B-4

599 vm

Coated

panicle

Coating

Diameter

1st

2nd

79 urn

79 //m

918 um

79 um

78 um

913 um

Fuel

compact

Outer diameter

Inner diameter

Height

Uranium content

35.85 mm

17.95 mm

35.98 mm

20 999g

35.98 mm

17.96 mm

36.01 mm

20.950g

OlH

Table 5 Uranium isotopic abundance

Isotope

23-HJ

23511

236u

238.J

Abundance(wt%)

B-2

0.0135

2.000

0.0016

97.985

B-4

0.0321

4.000

0.0252

95.943

Table 6 Atom densities in the fuel compact for cell calculation

Nuclide

Fuel kernel 234 y

235 v

236 u

238 JJ

16 0

10 B

>'B

1 st coating 12 C lo B

" B

2nd coating 12 c lo B

11 B

Atom density

[nuclei/(barn-cm)J

B-2

3.1907E-6

4.7067E-4

3.7494E-7

2.2768E-2

4.6485E-2

1.8386E-8

7.4473E-8

layer

5.97E-2

2.19E-9

8.51E-9

layer

9.38E-2

3.30E-9

1.337E-8

B-4

7.5355E-6

9.3499E-4

5.8655E-6

2.2143E-2

4.6183E-2

1.8263E-8

7.3973E-8

5.92E-2

2.08E-9

8.43E-9

9.38E-2

3.30E-9

1.337E-8

Nuclide

1st and 2nd

>2C 10 B

" B

Atom density

[nuclei/(barn-cm)]

B-2 B-4

layers homogenized

8.03E-2

2.82E-9

1.14E-8

Matrix graphite 12 C 10 B

II _ 11 B 16 0

14 N

8.581E-2

3.017E-9

1.222E-8 2.508E-6

9.399E-6

8.000-2

2.81E-9

1.14E-8

8.481E-2

2.982E-9

1.208E-8 2.599E-6

9.741E-6

8 -

'l I M I i C . , 1 , ni :<

Table 7 Atom densities for homogenized

fuel compact [cf. Fig. 8(b)]

Nuclide

234 TJ

235 u

236 u

238 Tj

16 0

10 B

" B 12 c 14 N

3 - j

1

3

4

I

7

6

Atom density

[nuclei/(barn-cm)]

B-2

663E-7

.929E-5

13OE-8

.9002E-3

882E-3

256E-9

724E-8

750E-2

618E-6

B-4

6.250E-7

7.755E-5

4.865E-7

1.8369E-3

3.832E-3

4.218E-9

I.708E-8

7.675E-2

6.858E-6

Central hole is not smeared.

One end cap is homogenized.

Table 8 Average number of coated

particles in a fuel compact

[cf. Fig. 8(b)]

Compact type [Particles/Compact]

B-2 type

B-4 type

2.002E+4

2.0406E+4

Table 9 Atom densities for graphite [cf. Figs 8(a), (b)]

12 c 10 B

" B 16 0

>H

Atom density [nuclei/(barn-cm)]

Graphite sheath

and end cap

7.45IE-2

1.146E-9

4642E-9

8 869E-6

1.232E-5

Graphite

assembly

8.356E-2

1.285E-9

5.206E-9

8.837E-6

1.225E-5

The atom densities are obtained from real

material density of graphite diluting with

volume of small clearances for rod or

compact insertion and block pile-up.

- 9 -

.! \ I \ K I I •

Table 10 Assembly temperature and number of fuel rods in the core

Step

1 2

3

4

5

Temp.

(°C)

25.5

71.2

100.9

150.5

199.6

VH1-HP

Fuel i

B-4

288

288

288

288

288

rods

B-2

0

0

0

0

0

Temp.

(°C)

8.0

200.3

VH1-HC

Fuel i

B-4

288

288

"ods

B-2

0

144

The numbers of fuel rods given above are the sums of

those in movable and fixed half assemblies

Table 11 Requested calculation items

Item

Cell calculation

Reaction rate

Spectral indices

Whole reactor calculation

keff

Reaction rate

Spectra! indices

Neutron balance

Fission distri.

Temperature coeft.

Step 1

X

X

X

X

X

X

X

X

X

X

VH1-HP

2

X

X

X

X

3

X

X

X

X

-X—

4

X

X

X

X

5

X

X

X

X

X

X

X

X

X

X

VH1-HC

1

X

X

X

X

X

X

2

X

X

X

X

X

X

X

X

X

X

A (Generation time) x x

10

.1 \ h i . I . ,• , i ' . . , | , '.i I

Table 12 Experimental keg- values for various assembly temperatures

Step

1

2

3

4

5

VH1-HP

Temp.( °C)

25.5

71.2

1009

150.5

199.6

keff

1.008

1.001

0.996

0.987

0979

VH1-HC

Temp.( °C)

8.0

200.3

keff

1.010

0 998

The ^ /va lues are corrected for loading irregularities

and for the neglection of fuel rods in partially loaded blocks.

Table 13 Experimental values of temperature coefficients of reactivity

for successive temperature ranges (VH1-HP)

Temp.

25.5

71.2

100.9

150.5

25.5

range

to 71.2

to 100.9

to 150.5

to 199.6

to 199.6

Temperature coefficient

of

(1

-1

-1

-1

-1

-1

reactivity

.56

.79

.81

.77

.73

The coefficient values are excluded by the effects of,

1) fuel rods in partially loaded blocks

2) expansion of assembly and air in the assembly

3) assembly fixing steel frames.

- 11 -

. l A I - . K I l i . i l . i C . i l , - ' . I I H i ; !

Tabie 14 Constants for the benchmark

Mass number

Air contents

Gas constant

Normal state

JH 10 B

" B 12 C 14 N 16 0

234 u

235 u

236 TJ

238 L ,

N2

O2

Avogadro's number

1.007825

10 01294 (19.8 wt%)

11.0093! (80.2 wt%)

12.00000

14.00307

15.99492

234.0409

235.0439

236.0456

238.0508

75.51 wt%

23.01 wt%

R. 31441 J/K/mol

T=273.16K

P=l 01325x10J/m

Av=6.022045E23

12-

Fixed half assembly Movable half assembly

Steel frame

Heat insulaling cover

, SRD hanger

. Safety rod driving mechanism

\ Control rod driving mechanism (CROM)

Heat insulating table

Fig 1 Bird's eye view of the assembly

Control rod simulation block -

Reflector block

Fuel block

Steel frame with heat insulator and cadmium sheet

Heat insulating (able

Circles in core and reflector indicate graphite rods The rods in core can be replaced with fuel rods, while those in reflector can be replaced with heater rods

Hu 2 Cross section of the assembly

. I A K H I I > ;11.• i ( • . , , ! • • <M UVA

24

1200

Unit : mm

065.5

oodoo OOOO

Fig. 3 Cross section of a graphite block

047.2X18

Pitch 65

End cap

-720 + 2(Stack margin)—

T •Graphite sheath

•-(•• • • • ' • • • • • . | i dfe (1) Real shape

727-

Fuel compact •

, , ; - . . . . ; < ; . . .„. ,_, . , . , ;^,o , , , .Air. , .: Idl

dl d2 d3

Unit : mm

JbL _ ?.-l 17.95 17.96 35.85 35.98 47.20 47.20

d2d3

Treated as reflector (2) Calculation model T Core mid plane

Fig. 4 Cross section of a fuel rod and its calculation model

1 st layer

Low density carbon

2nd layer

His '•• i.'ensity

a.-bon

Diameters are given in Fig 8(a).

Fig. 5 Cross section of a coated particle

- 14 -

• I A K K I ] ) . i i .1 !tl ill: ',

Unit : mm

B-4 fuel rod

Reflector region

Core

727

1200"

region

•727

1200

1200

2400

t Core mid plane

Fig. 6 Core loading pattern for VH1-HP and the first step of VHl-HC

Unit : mm

Reflector region

Core

727

B-4 fuel rod

B-2 fuel rod

1200

region

727

1500

-1200

1

2400

Core mid plane

Fig 7 Core loading pattern for the second step of VHl-HC

- 15

• l A K h ' l ] J . - 1 1 . - 1 < • « n i t - > l - l d i n

(a) Cylindrical reactor model

Region

Inner reflector

Fuel l(B-4)

Fuel 2(B-2)

Outer reflector

Diameter(10"2 m)

VH1-HP VHl-HC(200 °C)

31.50 31.50

113.58 113.58

137.32

252.02 252.02

Outer reflector

Inner reflector

Fuel l(B-4)

Fuel 2(B-2)

(b) Macro cylindrical cell model

(Number 2 heterogeneity) Fuel compact

Air

Fuel compact

Sheath

Block equivalent

Diameter( 10"-5 m)

B-2

17.95

35.85

47.20

90.94

(c) Micro sphere cell model

(Number 1 heterogeneity)

Kernel

1st layer

2nd layer

Matrix equivalent

B-4

17.96

35.98

47.20

90.94

Diameter(10-6m)

B-2

602

760

918

1374

B-4

599

757

913

1370

Sheath

Kernel

2nd layer

Block equivalent

1st layer

Matrix equivalent

Fig. 8 Examples of calculation models

- 1 6 -

. l A K I V l h . i i . i ( ' . " ! . • H I

O) O (O) (Q

Fuel block Graphite

Fuel compact

Air

Graphite sheath

Fig, 9 Accurate cell calculation model

Calculation mode!

mmmm 9 A«oK5Mb«n«dS*So«

(•) u») »)/P • O\« • • • / ' - ) • °\*(«is) is)/ \

® Fuel rod {2% EU)

• Fuel rod (4% EU)

• Safety rod hole

• Control rod hole

® Heater

0 BFJ counter

Fig 10 Actual core loading for a core corresponding to the second step of VHl-HC

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