SLAROM: A Code for Cell Homogenization Calculation of Fast

JAERI 1294CM

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SLAROM: A Code for Cell HomogenizationCalculation of Fast Reactor

December 1984

Japan Atomic Energy Research Institute

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Board of Editors

Takumi Asaoka

Masashi lizumi

Hiroshi Kawamura

Keizo Makuuchi

Hiroshi Okashita

Naomoto Shikazono

Yasuo Suzuki

Takehiko Yasuno

Shigeru Mori (Chief Editor)

Miyuki Kagiwara

Michio Ishikawa

Takuji Komori

Yoshio Murao

Kazuo Sato

Junichi Shimokawa

Masaoshi Tanaka

Mitsuo Yokota

Muneo Hand*

Akihiko Ito

Hiroshi Kudo

Takao Numakunai

Masayuki Sato

Nobutake Suzuki

Hirokazu Umezawa

JAERI U i U - K i ,

(X319-11

JAERI reports are reviewed by the Board of Editors and issued irregularly.

Inquiries about availability of the reports should be addressed to Information Division

Department of Technical Information, Japan Atomic Energy Reseat ch Institute, Tokai-mura,

Nakagun, Ibaraki-ken 319-11, Japan.

©Japan Atomic Energy Research Institute. 1984

JAERI1294

SLAROM: A Code for Cell HomogenizationCalculation of Fast Reactor

Masayuki Nakagawa and Keiichiro Tsuchihashi

Oepirtment of Reactor Engineerini, Tokii Research Establishment


Tokai-raura, Naka-fun, Ibaraki-ken

Received September 10,1984

Abstract

A revised version of the SLAROM code has been developed. The main function ofSLAROM is to perform the cell homogenization calculation of a fast power reactor and a fastcritical assembly. The code uses the JFS2 or JFS3 type cross section set as a multi-groupcross section library.

The region dependent effective cross sections are calculated by taking account of theheterogeneity effect of resonance shielding for heavy nuclides. The integral transport equationsare solved by using the collision probability method. SLAROM installs collision probabilitycalculation routines for various geometries encountered in a fast reactor analysis. The effectivemultiplication factor (£<(r) calculation or buckling search mode is available. The cell homo-genized cross sections are obtained by weighting with the fine structure flux and volumes.The calculation of anisotropic diffusion coefficient is based on the Benoist's definition withuse of the directional collision probability. The averaged macroscopic and microscopic crosssections are saved on the Partitioned Data Set file with a unified format. In addition to thecell calculation, another module is equipped to solve one dimensional diffusion equations innormal and adjoint modes. The fluxes obtained by this module can be used to collapse thefine group cross sections into the broad group structure. The perturbation calculation is alsoavailable.

This report describes the calculation^ method adopted in the SLAROM code, inputdata and job control statements instructions, structure of the code, file requirement andsample input and output data. Since the input data are punched in a free format, users will beeasy to prepare them. The description of auxiliary programs is «!ven in Appendix for a helpof the data handling on the PDS file.

Keywords: Cell Homogenization, Fast Reactor, Multi-group Constants, Effective Cross Sec-tion, Integral Transport Equation, Collision Probability Method, HeterogeneityEffect, Anisotropic Diffusion Coefficient, Group Collapsing, Cluster Model.

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SLAROM:高速炉用格子均質化計算コード

日本原子力研究所東海研究所原子炉工学郵

中川正幸，土橋敏一郎

( 1984年9月10日受理)

要旨

JAEa.ll2M

SLAROMコードの改訂版を開発した.SLAROMの主は樋能は.高適炉や高遺.界集合体の修子均質

化計算を行うととである.本コードは.多醇断面積ライプラリーとして JFS2又はJFS3聖断面積セッ

トを用いる.

~綱相自の実効断面積は.・4富掴に対しては共鳴遮厳因子'1:対する非均質効県を考.して針'草される.

積分型愉送方担式は.衝突・.法によ q て解<.SLAROMコードには.高遺炉の1)併で必畏となる掴

々の形状の倫子'1:対する衝突・.針鱒ルーチンが組込まれている.体系の実効泊倍.(t副}は入力さ

れたパックリング'1:対し求められるか.あるいは.界凋盤により 1と怠るようにItJ草される.セルの崎

質化断面積は.傾峨積分された中性子旗を・みとして求められ.非等方鉱散係敏l孟Benoiatの定.lCaづいて計算される.乙れら平均巨観及び..断面積は.p町 Fァイル11:統一形式で醤えられる.梅子計

算の他にも.一次元鉱般方檀弐を解いて中性子東と随伴中性子衆を求めるモジaールが含まれており.

乙れらの中性子東は.断面積の積約のために周νるととができる.また一次領動計算も可能である.

本報告は.SLAROMコードで用いられている計算法.入力データとジョプ制.文の観明.コードの

構成.ファイル使用法及び例・の入出力について記述している.特に.入力データはフリーフォーマッ

トで与えるので使用者の労力を歯車らすととができょう.補助プログラムに関する脱明が P凶ファイル

のデータ取級いの一助とするために付録で与えられている.

JAERI1294

Coda Abstract

1. Program Name: SLAROM2. Computer for which Program is Designed and Others on which it is Operable : FACOM

M-200, FACOM M-3803. Description of Function : SLAROM solves the neutron integral transport equations to

determine flux distribution raid spectra in a lattice and calculates cell avenged effectivecross sections.

4. Method of Solution : Collision probability method for cell calculation and 1 D diffusionfor core calculation.

5. Restrictions : Variable dimension is used throughout the program so that computer corerequirements depend on a variety of program parameters.

6. Running Time : It varies with geometry option and number of spatial regions. An infiniteplate geometry problem with 14 regions requires about 30 sec CPU on a FACOM M-380.

7. Unusual Features of Program : PDS files are used to keep the macroicopic and micro-scopic cross sections, etc.

8. Related and Auxiliary Program : Cross section library of JFS2 or JFS3 type which maybe generated by the TISM-PGG code. The MIX code to compote macroscopic crosssections and the PDSDMP code to print out data saved in PDS File.

9. Status: In use.10. References: JAERI-129411. Machine Requirements : Core requirements depend on problem complexity but virtually

any reasonable problem may be executed wi+hin 1 M bytes core memories.12. Programming Language Used : Fortran 77 and one assembler language routine.13. Operating System or Monitor under which the Program is Executed : FACOM OS IV14. Any Other Programming or Operating Information or Restrictions : A PDS (Partitioned

Data Set) file is used with undefined record format.15. Name and Establishment of Authors :

M. Nakagawa and K. TsuchihashiDepartment of Reactor EngineeringTokai Research Establishment, JAERITokai-mura, Naka-gun, Ibaraki-ken, 319-11, Japan

16. Material Available : The present report

JAEKI1294

CONTENTS

1. Introduction 12. Solution of Integral Transport Equations by Collision Probability Method 3

2.1 Multi-Group Integral Transport Equations 32.2 Calculation of Collision Probability 5

2.2.1 Boundary Condition , 52.2.2 Collision Probability for Slab Lattice 62.2.3 Collision Probability for Annular Cylindrical Lattice 82.2.4 Collision Probability for Two Dimensional Cylindrical Lattice 9

3. Cross Section 103.1 Cross Section Library • , 103.2 Effective Cross Section for Material Region 103.3 Interpolation Method of Shielding Factor for Background

Cross Section <H and Temperature T II3.4 Cross Section Output of SLAROM 12

4. Guide for Input Data Preparation 164.1 Free Format 164.2 Description of Input Data 174.3 Detailed Noteson Input Data 254.4 Job Control Statements 27

5. Structure of SLAROM 335.1 Calculation Flow 335.2 Function of Subroutine 415.3 Program Tree of SLAROM 50

6. File Requirements 546.1 PDS File 546.2 Cross Section Library File 566.3 Auxiliary Files 60

7. Sample Input and Output 647.1 One Dimensional Slab Cell 647.2 Square Cluster of Pin Rods 64

8. Comparison with Monte Carlo Calculation 758.1 Voided Pin Calandria Problem 758.2 Infinite Plate Cell Problem 75

9. Concluding Remarks 78Acknowledgments 78References 79Appendix : Auxiliary Programs 80

JAEM1294

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JAERI 12<H

1. Introduction

Many fast critical assembles have been built to provide physics data necessary for thedesign of fast power reactors. Though the power reactors consist of hexagonal fuel sub-assembly with uniform compositioned fuel pins, most fast critical assemblies consist ofheterogeneous plate cells including plates of metallic or ceramic fuel. Thus, although theaverage composition of the power reactor and its simulated critical assembly may be identical,there are significant differences in the internal arrangement of the component elements.Consequently, experimental data obtained in the various heterogeneous environment shouldbe transformed into the power reactor condition. Hence the heterogeneity effect should beaccurately taken into account in both analysis of critical assembly and power reactor.

In usual procedure of analysis, at first the cell calculation is performed to obtain cellaveraged effective cross sections prior to the whole core calculation. Some computer codeihave been developed for this purpose. The original version of SLAROM1' completed in 1974is one of such codes. However, most of them have only restricted functions concerning avail-able group constant sets, variety of cell geometry and efficiency of data handling, etc.. Inorder to overcome such restrictions, the revised version of the SLAROM code has been de-veloped.

This report describes a detail of the revised version of the SLAROM code. SLAROMhas been developed to perform cell homogenization for various lattices appearing in fastcritical assemblies and fast power rea-tors. The code produces cell averaged effective crosssections starting from the multi-group cross section library. As a standard cross section library,SLAROM uses the Bo darenko type group constant set JFS-22) or JFS-33> which have beenproduced at the Japan Atomic Energy Research Institute (JAERI).

In the cell averaging process, the heterogeneity effect due to the lattice structure shouldbe taken into account. The heterogeneity appears in the resonance energy region through theresonance absorption of heavy nuclides and in the fission source energy region, which causes aflux variation from one material region to another. The heterogeneity effect on resonanceshielding is considered in the calculation of background (admixture) cross sections by usingthe rational approximation. The effective cross sections of each material constituting the cellare calculated from the infinite dilution cross sections and the heterogeneous shielding factorsfor heavy isotopes and the homogeneous ones for moderator or structural materials. On theother hand, the fine structure flux in the cell are obtained by solving the integral transportequations based on the collision probability method. SLAROM installs the collision proba-bility calculation routines for various lattice geometries. The multi-group equations are solvedin either an effective multiplication factor (Ar.ff) or buckling search modes. The leakage fromthe cell is taken into account by adding the pseudo-absorption term DB* to the absorptioncross section. The cell averaged macroscopic and microscopic cross sections are calculated byweighting with the volume times fine structure flux of each region. The diffusion coefficientshave direction dependence corresponding to the heterogeneous structure of the cell. In thatcase, the code can produce anisotropic diffusion coefficients based on the Benoist's defini-tion4).

In addition to the cell calculation, there are included in the code modules to solve onedimensional diffusion equations in normal and/or adjoint modes. The flux obtained can beused to collapse the macroscopic and microscopic cross section into the broad group structure.

2 SLAROM: A Code for C ^ HombpnteaticM Calculation of Fut Reactor MEM 1294

A number of energy groups significantly affects computation economy, especially in multi-dimensional transport calculations of whole cores, hence an appropriate number of croupsshould b? selected with a consideration of accuracy. The perturbation calculation mode isalso available.

SLAROM consists of six blocks PREP, PATH, PIJF, EDIT, RATE and EIND. The inputdata are required for each block. The calculation proceeds in the order specified by the inputdata. The each block mainly has the following functions;

PREP calculates region dependent effective multi-group cross sections or homo-genized ones,

PATH calculates the collision probability,PIJF solves the multigroup integral transport equations by using the matrix inver-

sion method and the outer iteration,EDIT calculates the cell averaged cross sections and the diffusion coefficients,RATE calculates the in-cell reaction rate distribution, andEIND solves a one dimensional diffusion equation and collapses the crow sections.The original version has been revised in the present one mainly in the following parts;

addition of available cell geometry, addition of routines to calculate in-cell reaction ratedistribution, change of format in PDS file and adoption of variable dimensions.

SLAROM adopts a free format for almost all the input data, so users will be easy toprepare them. The output cross sections are saved in a PDS (Partitioned Data Set) file, ofwhich member name is composed of six alphabetical or numeral characters defined by users.Some utility programs are available to handle the data saved in PDS files. The format of crowsection data saved can be converted by using the interface code JOINT** into the ones re-quired in various neutronics calculation codes (ex. CITATION, ANISN, TWOTRAN2, PHF.NIXand CIPER codes). We recommend to use the JOINT code together with SLAROM.

This report describes the calculation^ method used in SLAROM in Chapters 2 and 3,detailed instructions for input data preparation and setting up of job control statements inChapter 4. The brief description of calculation flow and functions of subroutines is also givenin Chapter 5. The file requirement is shown in Chapter 6 for the cross section library, PDS fileand auxiliary files. The sample input and output lists are shown in Chapter 7. The results ofvalidation tests of SLAROM are described in Chapter 8 where a pin square cluster and a platecell are tested against the Monte Carlo calculation.

JAERI1294

2. Solution of Integral Transport Equations by Collision

Probability Method

2.1 Multi-group Integral Transport Equation

SLAROM calculates the spatial fine structure of neutron flux in a cell by soliving themulti-group integral transport equations. Among many solution methods for the transportequation, the collision probability method is accurate and not time-consuming if the scatteringis almost isotropic and a thickness of each material region consituted a cell ;s smaller thana mean free path of neutron. At the first, the derivation of multi-group transport equationwhich is solved in the code is briefly described below.

The multi-group form of integral equation is written as follows:

. a) =jr j ^ ~ no, a.) Qt{ f'. a)

[ l ^ ^ ] (2.1)

wheref = position variables,g — energy group index,O = angular vector,0,(r,Q)= angular flux,Q,(r, O) = source term by scattering and fission,£,_, = total cross section,r =r-Ra,,R = \r-r\ .V = volume of a cell.By integrating Eq. (2.1) over Q , we have the following equation for the total flux **((r),

)=J v - j=^p Q,(T) exp[-J#(r. ? ' ) ] . (2.2)

where the optical path length l,( r. f") is introduced by

(2.3)

The averaged flux of region j in a cell is obtained by integrating Eq. (2.2) over the volume V,,

V'*'=l*fT'1 f Q(r) "Pt-^ ' r» - (2.4)where the group index £ is suppressed, and the averaged flux *j is defined as,

We introduce the collision probability that a neutron emitted uniformly and isotropicaily inthe i-th region will suffer its first collision at the j'-th region as follows;

SLAROM: A Code for CeU Homofeniation OkmUtlon of F»«t Re»ctor JAERI1294

( 2 5 )

When each region of a cell is small compared with a neutron mean free path and the crosssections are constant in the region, we can assume that the neutron flux and the source distri-bution are flat over each region. By substituting Eq. (2.5), Eq. (2.4) can be rewritten as

HuVi*,= ZViPijQi (2.6)i-i

The source term is explicitly presented as

where Y.V , T,fn~' and 1, M*,, are the scattering matrix of elastic, inelastic and n, 2n

scattering, respectively, x', fission spectrum, and " £ / , production cross section. The

neutron conservation law requires the following relation in case of infinite number of cells:

Sfi;=l (2.8)/-i

Equation (2.6) can be written in the form of matrix equation of the volume integratedflux and source as follows;

£*=PQ. (2.9)

where S, 4 and Q are N dimensional vectors and Pis Nxff order matrix. For the criticalproblem, the eigenvalue k can be obtained by solving the eigenvalue problem,

2t=\PQ (2.10)

Consequently, the flux # can be easily calculated by the direct matrix inversion method ifPis factorized. Since Eq. (2.9) is given for each energy group, the neutron flux can be obtainedby solving these equations successively from the highest group to lower groups, where theslowing down source is calculated from the solution of the higher groups, because the up-scattering is not treated in the fast reactor calculation. After the neutron flux are obtainedfor all the regions and the groups, the fission source term and the effective multiplicationfactor are recalculated. Thus the v. j.;er iteration is carried out until the convergence criteriais satisfied.

When the system is finite, the neutron leakage from a cell should be taken into account.For a large system, the fundamental mode approximation may be used and the averagedleakage from the system is represented by DB'+ where B' is the critical buckling. In SLAROM,this term is added to the absorption cross section as a pseudo-absorption. If the critical buckl-ing is unknown, this value can be searched in the code.

In order to take account of the anisotropic scattering effect, the diagonal transportapproximation can be adopted by an option. In this case, the total cross section is replacedby the transport cross section defined by

E « , , = S u m H f t t i & « ? < f' (2.11)

,,,• — Sum Ni K.otji Pjitj} ,

where i stands for region and / for nuclide. The transport cross section is used in the calcula-

JAEXI1294 2. Solu Jon of Integral Tnuuport Equation! by CollMon notability Method 5

tion of collision probability,

2.2 Calculation of Collision Probability

The collision probability given by Eq. (2.5) is calculated for each geometry of a cell.The calculation method of the collision probability is fully described in Ref. 6, hence thefinal forms are shown below. In the SLAROM code, the anisotropic diffusion coefficients aredefined basing on the Benoist's formula4' unconnected for an absorption term, where thedirectional collision probability is computed by using the formula,

where * stands for direction.The available geometry for cell is as follows (see Fig. 4.1);

1. one dimensional sphere,2. one dimensional slab,3. one dimensional circular cylinder,4. square devided by concentric annuli,5. type 4 with the divisions by the equal azimuthal angle pitch of 22.5 degree,6. hexagon divided by concentric annuli,7. type 6 with the division by the equal azimuthal angle pitch of 15 degree,8. square pillar with octant (45°) symmetry,9. square cluster (type 8 with square arrays of pin rods),

1C cylindrical cluster (type 3 with annular arrays of pin rods),11. cylindrical cluster without angular periodicity (type 10 without angular periodicity,

and with and without the division by sectors),12. hexagonal cluster (type 6 with asymmetric annular arrays-oi pin rods and the

division by sectors,13. rectangular pillar divided by xy coordinates,14. hexagonal cluster divided by hexagons.

2.2.1 Boundary Condition

An isotropic (white) reflective, periodic (perfect) reflective and vacuum (black) boundaryconditions can be chosen in the calculation of collision probability. The best choice of themmay depend on geometry, accuracy and computation economy. When the perfect reflectivecondition is used, a neutron passes straightly until it suffers a collision even if it crosses a unitboundary. In this case the collision probability is calculated by tracing over a number of cellsuntil the neutron flight path length is over eight mean free paths.

Under the isotropic condition, on the other hand, the neutron path is traced only in aunit cell, and the probability Pit that a neutron born in the region i, collides for the first timeat the outside of a unit cell, is obtained from the formula,

where X , S and Rs are optical path length, outer surface and distance to surface, respectively.On the other hand, by denoting the probability that the isotropically incident neutron

collides for the first time in the region s asQ.,, then the collision number in the region i is

given by - j 0,, , because the current into the region is -^ when the uniform flux 4 is incident

e SLAROM: A Code for Cell HomofetrfxMJon Ctlcuktion of Fut Retctot JAEM1294

isotropically on the surface 5 of the cell. From the reciprocity theorem we get the followingrelation;

0.. = - ^ £ t.iPi.- (2.13)

Furthermore, we represent the probability that an isotropically incident neutron escapesfrom the cell without suffering any collision as Q»;

<?..= 1 - SO . , (2.14)y-i

Consequently, the collision probability f.y is written by using the collision probability inthe unit cell P'j as

*/=*« +ft. izfe, • "' <2 1 5>The computation time is required much more for the perfect reflective condition. In this

case, however, a sufficient accuracy will be achieved.

2.2.2 Collision probability for sltb lattka

Tne collision probability for one dimensional infinite slab lattice shown in Fig. 2.1 iscalculated by using the exponential integral function £<•(*) as follows; '

Pu= jj-lEi,Uii)-Ei,Uii+)ii)-Et,aii+Xi)+Ei,Uti+xt+ii)]. for i*rj .

(2.16)

and

P,,= l - - r - [&,(0)-E, ,a , ) ] . fo r i= ; (2.17)

where <ti and <*/ is the optical thickness of region t and j , and X» that in between regionsi and j as shown in Fig. 2.1.

Ei,(x) function is defined by

(2.18)

and the following recurrence relation holds

£,„(*)= JjS.,,-1 Or )dx . (2.19)

when the optical thickness of region i or j is small, the numerical integration of Eqs. (2.16)and (2.17) become inaccurate, hence we use the following differential form derived from therelation Eq. (2.19),

a) J,<0.001 J ; ^ 0.001

Pu= £[«.««>-*.(»«+*/+-£)] • <2-20>b ) i i SrO.OOl Xj< 0 . 0 0 1

(221)

c) Xt< 0 .001 ,(>< 0 .001

2. Solution of Intefnl Transport EqutttoM by CoOUoa Probability Method

P - J - FP.,- 2 X

and

The escape probability P,. is calculated by the formula,

where

Pi, =

«•=£

(2.22)

( 2 2 3 )

(2.24)

In the following, we show an explicit form of the directional collision probability fora slab lattice. Since the explicit form of Ol is given for the rectangular coordinate as

Q\ = sin'0 cosV .

O*, = sin'9 sin'V .

Q\ - cos'0

where 0 is angle to the t axis and V azimuthal angle, the perpendicular directional collisionprobability is written ?s

and

u, =1—^-[&«(0)-

for ii •¥ j

for i=j.

(2.25)

(2.26)

Infinite slab Annular cylinder

• i*l

X,

j - l j

Fit. 2.1 Neutron pith in infinite dab.

X; < f,

Fli. 22. Neutron pith in innulv cylinder.

SLAROM: ACode for CeUHomogenkitionCtlculition of Fut Rwctoi JAER11294

The pararell directional probability is easily obtained by using the following relation,

= jPa, + f (2.27)

2.2.3 Collision Probability for Annular Cylindrical Lattice

The collision probability for annular cylindrical lattice with infinite length (Fig. 2.2) ispresented by using the 3rd-order Bickley function as follows:

Pa =

i * j (2.28)

where

i-l

2= Si-i

s4-1

for n<r) ,

andi-l

S »̂ for r,

For the case «=/, Eq. (2.28) is reduced to the following equation,

Pa = - ^ ^

where

-rr f ' dp[«.-2ftt'i *ri-l

(2.29)

The Bickley function of order n is defined by

Ki,(x) = Kc(.x) ,

where 6 is the angle between the flight line and the z-axis. If -I, and i, are small, the followingdifferential forms are used to reduce the numerical error,

Pa = - = ? — f ' ' dp iiij IKn «,;.) + KH U,i,)} . (2.30)

P., =

(2.31)

JAERI1294 2. Solution of Intagnl Tnmport Equation by CottWon Probability Method 9

When the isotropic boundary condition is chosen, the escapes probability is calculated usingthe following formula;

Pi. =

(2.32)where

H

Alt, 2mi ^11 *

• • I Af

litl = £ Xt+ £ 1̂

The directional probability is explicitly given for the cylindrical coordinate by using theexpressions.

O'r = 4" sin** .

3Accordigly, the probability is obtained by replacing the Kin functions by y K>**' •

2.2.4 Collision ProbAIIJty for Two DimMtioml Cylindriori U n t oThe collision probability in the cylindrical system with general shape of its cross section

and of infinite height (geometry 4, 5, 6, 7, 9, 10, 11, 12 and 14) is generally given by thefollowing formula;

(2.33)

Pa = . , / v f" dp f'"d* U,-/f , , (0) +Ki,Ui)l , (2.34)

where Xt, /, and ij are the optical path length between region i and i, of region « and ofregion j , respectively.

The escape probability Pio is given by

Pi. = 2J^ J^dpJ"d#iKis(.h,)-KisUi,+Xi)-\ , (2.35)

where /),, is the optical path length from the edge of region i to the surface of the system.As for the directional probability, the following formulas are similarly derived.

piir= . ! „ f" d/» f 1 "d#[f t .a . ) -#frta ,+i J ) -#r r t ( i .+ i>)+i f r t a,+ai+iy) ] .

(2.36)

)] . (2.37)

The method of double integration appeared in the collision probabilities is fully describedin Ref. 6.

10 SLAKOM: ACodeforCdtHomofMiiatioaCUMktioiiofFut Rftctor MEKI1294

3. Cross Section

3.1 Cross Section Library

SLAROM uses the Bondarenko type7' multi-group cross section set as a nuclear dttalibrary. At present three kinds of group cross section sets are available, that is, the JAERI FastVersion 2 types with a R-parameter and without it, and the JAERI Fast Version 3 type. TheJAERI-Fast Version 2 set*> is the first type and the JENDL-2B-70 set*> is the second one.As the third type set, the JFS3-J2 set3) and the JFS3-B4 set»> are available. These sets consistof infinite dilution cross section, fission spectrum and table of shielding factors which aregiven for parameters, background cross section o% , temperature T and mutual interferenceeffect R. The detail of energy structure, library format and code numbers of nuclides aredescribed in Chapter 6. The Ledgendre components of elastic scattering matrix are preparedas the library in order to take account of anisotropic scattering up to the ft order.

3.2 Effective Cron Section for Material Ration

When a calculation starts from broad group cross section set, it is necessary to preparethe effective cross sections for each constituent material of lattice or homogeneous media atfirst. The effective cross section is calculated from the infinite dilution cross section and theresonance shielding factor /« based on the table took-up-method,

of =«'• U . (3.1)

where x stands for reaction type. The value of /* is determined by an interpolation or anextrapolation from the tablulated values as a function of the background cross section ••and temperature T. The JAERI Fast set can also take account of the mutual interference effectbetween the different heavy nuclides by using a R paramei?r which is the ratio of the atomicnumber density of M i U to that of other nuclides. In this case, the R dependence of ft istaken into account in the calculation of of .

For the homogeneous mixture, the background cross section for nuclide * is calculatedby the formula

o? = SWV/fl" . (3.2)

where oT is total cross section of nuclide m.The resonance shielding factor in a heterogeneous cell is determined as follows. The

background cross section of the region in a heterogeneous ceil can be defined basing on theequivalence relation of resonance integral tetween the heterogeneous and the homogeneousmedia. By using the Wigner type rational approximation to the collision probability, thebackground cross section is defined for an infinite regular lattice as follows1**:

. (3-3)

where 5* and V* are a surface area and a volume of fuel region, respectively, "C" Dancofffactor, *a " Bell or Levin factor, and "A * a suffix of region. The value of « «.* is the backgroundcross section of fuel region given by Eq. (3.2). The Dancoff factor can be regorously obtained

IAERI1294 „ 3. QowSwttoo 11

by calculating the collision probability corresponding to a black limit of cross section in fuelregions. However, it is usually calculated with a good accuracy by using the approximateformula described below.

For the cylindrical rod array, the modified form of the Dancoff factor is used with Bellapproximation10* given by

C = l - r - r ' ( l - r )

1+E../S.(3.4)

where Zi is the macroscopic cross section of the diluent region and V, its volume. This formulacan be applied to the case in which the diluent region consists of the cladding, coolant andstructural material by homogenizing them.

For the plate lattice, the following expression proposed by Meneghetti1'1 is adopted;

C'£, s(Sum(S,r)»)+£,ii(Sum(S«r)/), (3.5)

where T is a thickness of region A or / . Each argument of the £» functions is the summationof the mean chord lengths over all the cell regions containing the nuclides of interest.

The appropriate value of the Levin factor would be expected to vary with a strength ofresonance and its procedures have been suggested for evaluating the Levin factor "«' for agiven resonance. However, to preserve the equivalence relation an averaged value of"«"must beused over a resonance selected to give the most accurate reaction rate. In practical cases offast reactors, the exact choice is not too important. We recommend that the reasonable valuesare 1.30 ~ 1.35 for a cylindrical rod cell and 1.15 ~ 1.25 for a plate cell.

The shielding factor of a non-fuel nuclide is calculated for the value of ••.which is ob-tained for the homogeneous mixture.

Formulas (3.2) or (3.3) are calculated iteratively until the shielding factors converge initself, however this procedure requires much computation time. Non-iterative calculation isfairly good in an accuracy and economical. We recommend the latter procedure in the cal-culation of oo.

3.3 Interpolation Method of ShMding Factor for Background Croat Section o0 andTampwaturt T

The shielding factors are tabulated for three or four values of o, and three temperaturevalues in the JAERI Fast Version 2 type set and are eight values of o, and four temperaturevalues in the JAERI Fast Version 3 type set. The interpolation methods adopted in the codeare different between them. The hyperbolic function is used for the former type and the cubicSpline function is adopted for the latter one. An accuracy and computation tune are comparedamong various interpolation schemes in detail in Ref. 12.

The interpolation by the hyperbolic function is made by using the formula:

(3.6)X = I

and the coefficients i t , B and C are given by

12 SLAROM: A Code for CeU HomogeoliiUoo Olculitioo of Fut Re«toi JAEM1294

R =A Ua- x») +Mx»-x,) +f,(xi-xi) '

c = (xl-xtKxt-x,Kx,-xl)(f,-ft)(A-/t)(J,-/l)

where / , , / , and / , correspond to the tabulated values of shielding factors at •« or T=x, ,xt and xt, respectively. This fonnula should be slightly modified depending on the form ofthe table.

On the other hand, the cubic Spline method uses a polynomial of order 3 which if writtenby

/(*)=

for *<*,

for x,

f»+B»(.x-x.)+Cn(.x-x,y , for x>x,

(3.8)

where the coefficients S., C, and Dt are obtained by solving the simultaneous equations forthe second order derivative of / , .

3.4 Cress Section Output of SLAROM

SLAROM can edit several types of cross sections in the calculations! step* at follows;PREP : macroscopic and microscopic cross sections for homogeneous medium, effec-

tive cross sections of each material regionEDIT : cell averaged macroscopic and microscopic cross sections, homogeneous or

anisotropic diffusion coefficientsEIND : group collapsed macroscopic and microscopic cross sections and diffusion

coefficientsThese cross sections are saved on the PDS file with a member name aisigned by users.

(1) Macroscopic cross section

The cell averaged macroscopic cross sections are calculated by the formula;

, (3.9)

(3.11)

(3.13)

JAERI1294 3. Cro«S«ctio» 13

T t f . • (3.15)

E*/=EEf,''#2V./E#:v1. , for /SI , (3.16)N n

where g, n and / stand for the suffix of group, region and the order of Legendre expansion,<t>n,V, are neutron flux and volume of region n .

The summation over n is carried out for the whole cell if INR * 0 (input in EDIT section)and for the assigned sub-cell regions, NR1 to NR2 if INR>0. If the input parameter ICASE(in PREP section) is set to be zero, the total cross section is replaced by the transport crosssection.

(2) Diffusion coefficientUsers can select the type of diffusion coefficients to be edited. The homogeneous dif-

fusion coefficient so called is defined by

or = S *JH/(3 • £ Efr..#: Vn) . (3.17)a •

The anisotropic diffusion coefficients are given by using the directional collision pro-bability described in Sec. 2.2,

i . . , J ) (3.18)i i •

and the averaged diffusion coefficient is

D't=±?:Dl . (3.19)

where k indicates direction. In the output of EDIT routine, D\ is calculated for plate androd cells as follows;

Of (plate) = (2 D,+DJ/3 , (3.20)

flf(rod) = (2-£>,+D.)/3 . (3.21)

In Eq. (3.18), the range of summation over i and j depends on the option INR as follows;

ISi., j£NR., for INR=0 ,

for INR = 1 ,

, NR1£;'£NR2. for INR=2I3)

(3) Microscopic cross sectionThe cell avenged microscopic cross sections are defined to conserve the total reaction

rate in the cell as follows;

vo, = Ei'O/AU.K./EAU.V,, . (3.22)II •

o, - Y.otN,*.V./T.N»i,V» , (OI=O/+«,+O.I+«,.+OM.) (3.23)* •

otr= HotrN.4uVn/'ZN.4,V. , (o , r=o,-£«, / ) (3.24)

M SLAROM: A Cod* for QB Hn«o>wlriHo« CUwtoMon of Put Rwctot JAEM12M

o. = T.o.N.i.V./'Z.Nui.V. , (3.25)• «

I (3.26)

(3.27)

. . (3.28)

(3.29)

o'..g-g-= T.o',,.t.t-Nm+mVJ'LN.*n. f o r / ^ 1 , (3.30)

o» = o<-»« . (3.31)

where the suffixes of group and nuclide are dropped and Nn stand* for the atomic numberdensity of an interesting nuclide in region n, #• neutron flux and V, volume of region *.

(4) Group coUapaedcroM sectionIn EIND routine, the macroscopic and the microscopic cross sections obtained above

are collapsed by using the regional neutron flux as a weighting function. The neutron fluxare obtained by solving the one dimensional multi-group diffusion equations shown below.

where

0 for slabp= \ 1 for cylinder

2 for sphere

WAI (

xt Sum vT.'Ag*t<r) + Sum S* f-.,* f(r) . (332)

= neutron flux,D't * diffusion coefficient,E!. f =* total cross section,it - fission spectrum,v£ / . f « v fission cross section,£!./•-* • scattering cross section from group g to K,

and i, / are suffix of region and group, respectively.For slab and cylindrical geometry, the leakage is taken into account by adding the pteudo

absorption term DB*. If the option for critical search is assigned, the dimensional search isperformed by varing the mesh interval of one region. For the eigenvalue calculation, outersource iterations are made until the convergence criteria are satisfied. We test the differencesof multiplication factors and the fission source distributions between iterations against thecriteria.

The collapsed macroscopic cross sections are obtained by the formula,

JAERI1294 3. CamStetkam IS

, (3.33)

where Vt is volume of region i,

* c = S *'. (3.34)

, (3.35)

(3.36)

where x stands for type of reaction,

t'mc gme

Dc= S D^'/« c . (3.38)1*0

The microscopic cross sections are similarly calculated except for the transport cross section.It is weighted with the flux if ITR - 0 (Input in EIND section), but weighted with *'f S fr ifITR * 1, that is,

o?r=(i; off*'/2fr)/(S#'/Ifr) . ' (3.39)

16 SLAROM: A Code fot Cell Homofeniiitfcm Calculation of Fut Re«ctor JAEKI1294

4. Guide for Input Data Preparation

4.1 FiMrormat

The SLAROM code reads data in the free format for integer and real type numbers byusing the subroutines, REAI, REAM and REAG which have been developed at JAERII4).By using this format, users can reduce labor and avoid troubles in preparing the input data.When the same data arc repeated or the data increase with the sam; interval, the input datacan be simplified by using the special characters. In the following, how to punch the data isbriefly mentioned.

(1) Basic rule of data punchFloating point number should be punched basing on a rule shown in the following;

S , V V.ES, V, ,

where S, and S. are siitn, V, and V, left and right side numbers of a decimal point, respec-tively, v, an absolute value of exponent and " ." a division of data.

The above representation is only a general rule, so the following items can be abbreviated,1. E ~ V5, if there is no exponential part.2. Si if the data is positive.3. V, if V, equals 0.4. V, ifV, equals 0.In place of the mark, one or more blank can be used. The following limitation must be sat-isfied.1. V, or " •" must be punched if + or - sign is punched.2. V3 must be punched if E is punched.3. A single number must be terminated in the columns 1 ~ 72 of one card.4. V2 must be less than ten figures.

(2) Function of special characters1. Repeat

N(D,, Dj, •, Dra), where N is a positive integer. This form indicates that m data ofD, ~ Dm are repeatedly punched in N times. M must be smaller than 30 and the data N( )must be punched in columns 1 ~ 72 of one card.

Example 2(1.0,1.5), 3(0.) indicates 1.0, l.S, 1.0, l .S.0. ,0. ,0.2. Addition

D, , N*D., where N is a positive integer. This form indicates that the following data arepunched,

D,, D,+D,, D,+2D,, D.+3D,. , D,+ND t .

N*D, must be punched in columns 1 ~ 72 of one card. Care must be taken that repeat andaddition are unable to use at the same time.3. End of array

/(slash)If / (slash) is punched after the array of data, the program interrupts reading the data,

then ckecks the number of words. If this number is more or less than the required number of

IAERI1294 4. Guide for Input Drt> FNptntion

words, the program prints an error message and stops. It is helpful for a check of input data topunch / at the end of each data array.

4.2 Description of Input Data

The input data for SLAROM consists of six blocks, PREP, PATH, PIJF, EDIT, RATEand EIND which are corresponding to the calculation steps described in Chapter 5. The headcard of each block presents the step name. A sequence of data blocks should be in an order ofthe calculation flow, but some steps can be repeatedly run in one job. The data are input in thefree format unless a format is not specified. The sample input data are shown in Chapter 7.

Section 1 PREP# 1 "PREP"(4H)# 2 Titled 8A4)# 3 1. NREG

2. NSCR= 0= 1

3. ICASE= 0= 1

4. IBSW

===

5. IGEOM

=6. IPR

=7. ITPE =

=>

8. MICOUT

<9. IPL

10. LNMAX

11. NRMAC12. IXCODE

012

01

01- 100

0N0

SLAROM Input Format

(1 ~ 4 column)TitleNumber of material region. (Enter 1 for homogeneous case.)Structure of cell.Symmetric cell.Periodic cell.Option for transport approximation.Diagonal transport approximation. £<r is used.aCross section selected here is used in the collision probabilitycalculation.Control of medium and criticality search.Homogeneous medium.Heterogeneous medium.Search critical buckling for heterogeneous case.Geometry of cell used in the calculation of effective crosssections.Slab cell.Cylindrical cell.Edit option of cross section.No.Effective cross section is printed out if IBSW = 0.JENDL 2B-70 (without R-parameter).JFS V-2 (with R-parameter) type.JFSV-3type.Edit option of microscopic cross section.No.Number of nuclides to be saved.All nuclides are saved.Pi order of Legendre coefficient for anisotropk scattering.Number of nuclide in library if ITPE <10.Set to be 0, if ITPE > 0 .Number of regions to edit their cross sections on PDS file.Code number of nuclide of which fission spectrum is saved.

IS SLAROM: A Code foi Cell Homofeniiation CUculatkn of Fut Reactor JAERI1294

If IXCODE = 0, the sv?raged fission spectrum of B 5 U and239Pu weighted with the atomic number densities is adopted(effective for the case ITPE > 0).Number of energy group.Code number of nuclide to be edited.Do not enter unless MICOUT > 0.Temperature (°K). If temperature depends on region, entera value greater than 10*. Then, the following card #6 isrequired.Bell factor.

(Recommendation; 1.20 - 1.2S for slab cell,1.30 for pin cell.)

Buckling value (B2). If IBSW^2, BSQ is replaced by thesearched buckling value. If energy dependent buckling valueis necessary, enter a value greater than 10*, then the followingcard #7 is required.Temperature of each region.Do not enter unless TE > 10*.Energy dependent buckling value.Do not enter unless BSQ > 104.Number of nuclides included in each material.Width of each region (cm).Code number of nuclide and its atomic number density in10*4 atom/cm3 unit. New region is begun on * new card.Member name of effective cross section to be saved on PDSfile for IBSW-0. Enter blank card if cross section is notsaved. Full name is composed by the rule described in Chapter6.1.

Do not enter the following cards 12 to 14 unless NRMAC > 0.Repeat the following data set by NRMAC times.

Region number.Comment.Member name of region-wise cross section.

(1 ~ 4 column)TitleTotal number of energy groups.Number of cross section material.Control of directional collision probability:Isotropic,Directional.Edit form of collision probability:

13. IMAX# 4 MELM(MICOUT)

# 5 1. TE

2. AINP

3. BSQ

# 6 TEG(NREG)

# 7 BSQG(IMAX)

# 8 NOELM(NREG)# 9 RMAX(NREG)#10 NCODE, DEN(NREG)

#11 ANAME(6H)

#12#13#14

IREGTitle(18A4)ANAME(6H)

Section 2 PATH# 1# 2# 3

"PATH"(4H)Title(18A4)1. NG2. NM3. IDRECT

« 1* 2

4. IFORM= 0= 1 Pa/Hi.

Enter IFORMstep.

1 if diffusion coefficient is required in EDIT

JAERI1294

5.

6.

7.#4 1.

IBSW

=>

IPREP

==

IPLIGT

=====

==

-

==s

01

01

12345

67

891011

4. Guide for Input D«t» Preparation 19

= 12

=:=:

2. NZ3. NR

4. IBOUNDa

=

=

5. NX6. NY

7. NTPIN

8. NAPIN

9. NCELL

10. IEDPIJS

S

1314

012- 1

01

11. NGR

Option of buckling search. Set the same value in PREP step.No.Search.InpUt option of cross sections.From PREP step.Read from PDS file.Pi order of Legendre coefficient for anisotropic scattering.Geometry of cell, (see Fij. 4.1)One dimensional sphere.One dimensional slab.One dimensional circular cylinder.Square pillar divided by concentric annuli.Type 4 with the divisions by the equal azimuthal angle pitchof 22.5 degree.Hexagonal pillar divided by concentric annuli.Type 6 with the division by the equal azimuthal angle pitchof 15 degree.Square pillar with octant (45°) symmetry.Square cluster (type 8 with square arrays of pin rods).Cylindrical cluster (type 3 with annular arrays of pin rods).Cylindrical cluster without angular periodicity (type 10without angular periodicity, and with or without the divisionby sectors).Hexagonal cluster (type 6 with asymmetric annular arrays ofpin rods and the division by sectors).Rectangular pillar divided by x—y coordinates.Hexagonal pin cluster divided by concentric hexagons.Total number of zone.Total number of region (the collision probability is calculatedfor region).Outer boundary condition of the cell:Isotropic (white),Periodic,Isolated (black),60° rotational (only for IGT * 12).Number of mesh intervals for the x or r division.Number of mesh intervals for the y or 0 division(forIGT=ll ,12,13) .Total number of pin rods (effective for IGT* 10, 11, 12 or14, calculated internally for IGT = 9).Number of rods in an array (for IGT = 9). Number of circularrings on which the pin rods are placed (for IGT = 10 and 14).Number of lattice cells traced by a neutron path (effectiveonly for IBOUND =1).Print control of collision probability.Skip,Print.Order of Gaussian integration for the radial integration. The

SLAROM: A Code foi Cell HomofMdzMkM Cilrahttai of Fast Reactor JAERI1294

# 5

# 6

# 7

# 8

# 9

#10

#11

#12

12. NDA

13. NDPIN

14. IDIVP

IS. IBETM

#13#14

computation time is proportional to this parameter. ForIGT = 8 and 9, the Gaussian integration is replaced by thetrapezoidal rule.Recommended value = 1, for IGT = 2

= 6 ~ 10, for others.Number of division of the range IBETM degree for the angularintegration.Recommended value = order of IBETM/2.After making the path table, the ratios of the numericallyintegrated volumes to the exact ones are printed out. Thedeviation of the ratios from unity should be less than a fewpercents. Users should adjust the values of NGR and NDA soas to be accurate and not to be time-consuming.Number of annular division of a pin rod for the case IGT *9,10,11,12 and 14.Control of zone division by RPP's for the case IGT • 9 ,10,11,12 and 14.

0 RPP's indicate the radial position of pin rods.1 RPP's play a role of RX's.2 RPP's divide the pin rod regions (no effect for IGT - 9).

Integer number to define the range for the angular integrationin degree. Rotational period (symmetry) should be taken intoaccount if any. That is, set IBETM = 45 in octant symmetricgeometry, and = 60 in hexagonal symmetry.

16. IPLOT Dummy. Enter IPLOT = 0.NREG(I), Do not enter if NR = NZ.I = 1, NZ Region number of I-th zone.MAR(I), Cross section material region of I-th region.I=1 ,NRNPIN(I), Enter only if IGT = 10 and 14.1 = 1 , NAPIN Number of pin rods in I-th array.RX(I), Radius of X-abscissa.I = 1 , N X + 1 RX(l) = 0.TY(I), Enteronly ifIGT= 11,12,13andNY> 1.1 = 1 , NY 9 for IGT =11,12.RPP(I), Enter only if IGT = 9 ,10,11,12,141 = 1 , NAPIN Radial position of I-th pin rod array for IGT = 9, 10, 14.

1, NTPIN Radial position of I-th pin rod for IGT « 11,12.THETAd), Enter only if IGT = 10,11,12.1*1 , NTPIN Angular position of I-th pin rod by degree.RDP(I), Enteronly if IGT = 9,10,11,12,14.I - l . N D P I N + 1 Radii ofannuU in a pin rod for IGT = 9,10,14.orRDHU),1 * 1 , NDPIN + 1 Radii of annuli in J-th pin rod for IGT = 11,12.J * l , NTPINDo not enter unless IPREP > 0.BSQ Buckling value (S«).KAI(6H) Member name of fission spectrum.

MERI1294 4. Guide for Input Data Ftapuatioii 21

#1S ANAME(6H) Member name of cross section.1 = 1, NM I corresponds to the material number assigned in MAR.

(NM < 30)

Section 3 PIJF# 1# 2

# 3

"PIJF"(4H)1. NGK

2. IFFG

3. IOFLXIOFLXIPRF -

-ICDF «

ITF -

= 0•• 1

•• 2

(1 ~ 4 column)The lowest energy group of fission source.NGK = 28 for JFS VI,NGK = 37 for JFS V2, JFS V3.Guess for neutron flux distribution.Flat source (skip).Fixed source.Enter NG*NR data.Option for flux output.

- ITF + ICDF+ IPRE102040

Enter ITF £4. ICONV

=====

ICONV = 35. IPTXEC

=6. IPT

7. IPTPIJf=

8. IPTFG

=1. ITMIN

2. ITMOUT3. EPSI4. EPSO

12345

Print.No.Card punch.No.Write on unit 4.No.

: 4 if EDIT step is required.Criteria of convergence.Activation.Slowing down.v* fission.Collision.Absorption.

is a strandard for an eigenvalue problem.

01

Control of cross section output for each region.No.Print.

nm (integer of two figures) write on unit nm.

00

00

00

Control of volume output.Print.No.Control of collision probability output.Print.No.Control of flux guess output.Print.No.Maximum number of inner iteration allowed per outer itera-tion (= 2).It is satisfactory to enter 2 for an eigenvalue problem.Maximum number of outer iterations (* 100).Convergence precision of inner iteration (* 1.0 E-4).Convergence precision of outer iteration (= 1.0 E-S).

22 SLAKOH: ACo(k forCcUHorootwiii«tio«Cilc»ktio«of Fut RMCtor JAERI1294

5. EPSG Extrapolation criterion (-0.01).6. RELG Initial extrapolation factory 1.4).If the input data are 0 or 0. for each parameter, the value in parenthesis is automaticallyset.

# 4 PHI(NR*NG) Initial guess of flux. Enter if IFFG = 2.# 5 IRXEC Control of input for activation cross section.

= 0 No.> 0 Read activation cross sections of IRXEC nuclides.

# 6 XEC(NG) Input data of activation cross section. Repeat IRXEC times.Enter only if I R X E O 0 .

Section 4 EDIT# 1 "EDIT"(4H) ( 1 ~ 4 column)# 2 1. IRPHI Input of neutron flux.

= 1 Read from card.- 2 Read from unit 4 (written in PIJF step).

2. IRP Input of directional collision probability.- 0 No.

Isotropic diffusion coefficient defined by Eq. (3.17) is cal-culated.

- 2 Read from unit 21 (written in PATH setp). Anisotropicdiffusion coefficient defined by Eq. (3.18) is calculated.

3. IEDXEC Control of output for cell averaged effective cross sections.IEDXEC = JPRINT + JCARDJPRINT = 0 No.

= 1 Print.JCARD = 0 No.

= 2 Card punch.4. INR Control of cell region.

= 0 Average over the whole cell.= 1 Average over sub-cell regions defined in Sec. 3.4.= 2 Average over sub-cell regions defined in Sec. 3.4.

5. MICED- 0 No effect.= 1 Microscopic cross sections are edited if IPREP * 1.

# 3 NR1,NR2,LM1,LM2 Assignment of sub-cell regions.NR1 Specify the first region of sub-cell.NR2 Specify the last region of sub-cell.LM1 Specify the first material of sub-cell.LM2 Specify the last material of sub-cell.The cell averaging is performed over the subcell regions (NRl ~ NR2), (LM1 ~ LM2).Do not enter if INR - 0.

# 4 PHI(NR»NG) Flux.Enter only if IRPHI * 1 .

# 5 ANAME(6H) Member name of cell averaged macroscopic and microscopiccross sections on PDS file. Enter blank card if cross section isnot saved. Microscopic cross section is saved only if MICOUT

JAERI1294

Section 5 RATE# 1 "RATE"(4H)# 2 Title(18A4)# 3 ANAME(6H)

Section 6 EIND# 1 "EIND"(4H)# 2 Title(18A4)# 3 1. NPROB

2. IP« 0- 1* 2

3. NPT

4.5.6.7.

8.

9.10.

11.

12.

#4 1.

2.

KM AXIMAXIDSLAPSE

NADJ

*

MXPRTMLAPSE

<

ITR

ICHI

ISYM=

ICEL-

012

00N > 0

01

01

1- 1

1- 1

(1 ~ 4 column)TitleMember name of microscopic cross section on PDS file. In-cellreaction rate is calculated with use of neutron flux obtainedin PIJF step.

(1 ~ 4 column)TitleProblem number of this case.Geometry option.Slab.One dimensional cylinder.Sphere.Total number of merit points. Number of mesh intervals mustbe an even number (NPT • mesh intervals + 1) and let* than100.Number of region.Number of energy group £ 70.Maximum number of slowing down group £ 29.Number of collapsed group. Enter 0 if cross section collapsingis skipped.Option of adjoint flux calculation.No (normal flux calculation).Normal and adjoint calculation.Adjoint calculation.Number of cases of perturbation calculation.Control of collapsing for macro- and microscopic cross section.If LAPSE * 0, MLAPSE has no effect.Only macroscopic cross section is collapsed.Macro- and microscopic cross sections are colapted.Additional N macro- and microscopic cross sections arecollapsed (#15 cards is necessary).Collapsing of o,T.Flux weight.4/Htr weight.Option of fission spectrum.Read from PDS file.Rtsd from card (#9 card is necessary).Boundary condition at the origin.#'(0) = 0.# ( 0 ) = 0 .Boundary condition at outer edge.

3. IB1R Control of region dependence of buckling.No dependence (one word for the whole reactor).

SLAKOM: A C o * for CHI H w a n ^ i t i o n Cilculittoi of F«t Kwrtoc JAEM12M

= - 1 Region dependent (one word for each region).4. IBG Control of energy dependence of budding.

Group dependent.Group independent.Control of criticality search.Dimensional search is performed.No.Control of output for cross section.No.Print.Control of output for flux.Print.No.Control of output for integrated flux.Print.No.

# 5 INTER(KMAX) Mesh number of outer boundary of each region. This valuemust be even number (The origin is 0).

# 6 KCTROL(KMAX) Control of criticality search region. Enter 1 for a critkalitysearch region and 0 for the others. Criticality search is per-formed for only one region. Enter only if ICRIT • 1.

# 7 IX(LAPEE) Boundary groups for collapsing. Enter the lower group numberfor each collapsed group. Enter only if LAPSE > 0.

# 8 1. EPS1 Convergence precision of eigenvalue.Convergence precision of flux at each mesh point.Lower limit of searched mesh interval Or).(Enter 0. unless ICRIT - 1)

4. DRMAX Upper limit of searched mesh interval ( i r ) .(Enter 1. unless ICRIT-1)

5. THETA Extrapolation Actor for outer iteration.Recommended value is O.S.

# 9 DR(KMAX) Mesh interval of each region (cm).#10 CHIL(IMAX) Fission spectrum. Enter only if ICHI-1.#11 ANAME(6H) Member name of fission spectrum on PDS file. Eater osOy if

ICHI * 0. Fission spectrum is stored in PREP step aad then,its member name is printed out.

#12 CNAME,DNAME(6H,4X,6H),(KMAX cards)Member name of macroscopic cross section.

CNAME Member name of cross section.DNAME Program name of cross section produced.

When this cross section is produced by SLAROM, DNAME isnot necessary. KMAX cards are required. The same membername can be repeatedly used.

#13 BSQ Budding value. Number of entries depends on the options IBGand IB IR.

IB1R=1,IBG--1 One word (enter 0. if IP « 2).IB1R-1JBG-1, IMAX entries.IBIR-1,IBG*-I, KMAX entries.

=5. ICRIT

==

6. IXPR==

7. IFPRS

8. IFLX--

1- 1

1-1

01

01

01

INTER(KMAX)

KCTROL(KMAX)

IX(LAPEE)

1. EPS12. EPS23. DRMIN

JAERI1294 ,_ 4.

IB1R=-1,IBG»1, KMAX*IMAX entries.Enter region dependent values (KMAX) from group 1 to groupIMAX.

#14 ANAME(6H) Member name of neutron flux to be saved on PDS file. Enterblank card if flux is not saved.

#15 ANAME(6H) Member name of collapsed cross section on PDS file. Enteronly if LAPSE > 0 .

#16 ~ #19 are skipped unless MLAPSE > 0.#16 Title(18A4) Title of collapsing calculation.#17 NREG Specify region number of flux to be used in additional collaps-

ing calculation.#18 ANAME,BNAME(6H,4X(6H)

ANAME Member name of cross section to be collapsed.BNAME Program name of cross section produced. When this cross

section is produced by SLAROM, BNAME is hot necessary.#19 ENAME(6H) Member name of the collapsed cross section.#16 *- #19 must be repeated by MLAPSE times.

Enter the following cards if a calculation of reaction rate distribution to required,otherwise enter one blank card.

#20 Title(18A4) ; "#21 1. NREG Number of regions to be calculated.

2. NUCLIDE Number of nuclides to be calculated.#22 IA(NREG) Region number.#23 NUC(NUCLIDE) Code number of nuclides.#24 CNAME,DNAME(6H,4X,6H)

Member name of microscopic cross section and program nameof cross section produced.

#25 CNAME,DNAME(iCMAX*MXPRTcardsX6H,4X>6H)CNAME Member name of macroscopic cross section in perturbed

system.DNAME Program name of cross section produced. When this cross

section is produced by SLAROM, DNAME is not necessary.Enter only if MXPRT>0.Member names are required for all the regions in perturbedsystem. Specify the same member name as the reference casefor the unperturbed regions. For the case of MXPRT> I, thereference case is always the same. The reactivity changes arecalculated for the differences of the macroscopic cross sectionsbetween the reference and the perturbed cases specified here.MXPRT sets of #20 (KMAX cards) are required.

4.3 Dataitod Notts of Input Data

This section gives the detailed definition of selected parameters and arrays. Some recom-mendations are also included.

(1) PREP step# 3card

SLAROM: i^fi>J»lbiCaHuMn|iirtralluiiOric«lirto«of FMCKwctOf 1AIM11M

2. NSCRThis is effective only for a slab cell. If the cell is symmetric at the center, the half of unitcell is described in this step.

3. ICASEICASE = 0 is a standard value if the Pi component of anisotropic scattering is not re-quired. If ICASE - 0, the transport cross section is edited in place of the total crosssection.

4. IBSWFor the case IBSW = 2, the group independent critical budding is searched in the range

7. ITPESLAROM can use three types of cross section library. Users should pepare the groupconstant set which is written in a binary mode. A detail of the library is described inChapter 6.2.

8. MICOUTThe effective microscopic cross sections assigned are saved on the PDS file.

9. IPLIf IPL > 0, the cell avenged (or homogeneous) Pi components of scattering matrix arecalculated by using the flux at a weighting function and saved on the PDS file. Note thatthese matrixes are not used in the cell calculation.

11. NRMACThe region dependent macroscopic cross sections are saved for the assigned regions.

# 9 cardRMAX(NREG)

For the cylindrical cell, input the region width not the radius.

(2) PATH step# 3 card

3. IDRECTIf anisotropic diffusion coefficients are necessary, set to be 2.

6. IPREPIf all the cross section used in this step are prepared in the preceeding PREP step, setto be 0. If IPREP - 1, the cross section are read from the PDS file produced already.

# 4 card1. IGT

Geometry of unit cell is illustrated in Fig. 4.1.2. NZ

NZ is a total number of geometrically smallest zones which are shown in Tabt* 4.1 foreach IGT. An example of numbering of zones are illustrated in Fig. 4.2.

3. NRThe collision probability and neutron flux are calculated for each region which consistsof one or more zones (NR £ NZ, and NR ̂ NM).

9. NCELLThis is the minimum number of lattice cells traced by a neutron free flight path. A recom-mended value of NCELL is NCELL • 2 for the geometry of assembly type i e . IGT • «, 9,12 or 14, or NCELL - 5 for IGT • 2 , 4 , 5, 6 or 7. Even if the neutron path is cvt off atthe calculations of collision probability at the first stage, it is renormatized to <Eq. (2.8). Computation time is proportional to the value of NCELL.

JAERI12M 4. (MfcteBvatlMalMpiutiMi IT

14. IDIVPIDIVP = 0 is a standard case where zone boundaries lie between pin rods. If IDIVP - 1,the moderator region is divided by the zone boundaries passing through the centers ofpin rods. When IDIVP • 2, the pin rods is also divided into two parts by the zone bound-aries. The option of IDIVP is illustrated in Fig. 4.1.

# 5 and* 6cardsNREGd) and MAR(I)

A sample is shown in Fig. 4.2 and Tabte 4.2 for IGT = 9 with 16 pin rods. The total zonenumber (NZ) is 41 as presented in the figure. The region number NR and material number,NM are 14 and 6, respectively, and NREG and MAR are tabulated below. In this model, thefuel pins numbered as 32 and 33 have the different composition from the others. The cahndriatube and the moderator region are treated as a single region, respectively. If tome zones aregeometrically and physically symmetric, it is recommended to assign the same region numberas shown in the table.

(3) EDIT step# 3 cardNR1,NR2,LM1,LM2

The cell averaging is performed over the sub-cell regions defined by these parameters.An example is shown below.

Region 1 2 3 4 5 6 7 8 9 10Material 1 1 2 3 1 2 4 4 1 1

Sub-cell

NR1 = 3, NR2 • 7LM1 = 1, LM2-4

Note that the region numbers must be sequential in the range NR1 ~ NR2, so it is incorrect toselect the regions 3, 4, 7 ,8 (without 5, 6) as a sub-cell. This option will be useful in a super-cell or a multi-cell problem.# In EDIT step, the neutron balance by isotopes is printed out if users set MKXHJT < 0 inPREP step.

(4) RATE stepIn this step, the in-cell reaction rate distributions are calculated for the reaction types,

absorption, fission and power distributions of the elements, MELM defined in PREP step.In the calculation, the region dependent effective microscopic cross sections are used togetherwith the cell averaged effective cross sections. Preceeding this step, PREP, PATH, PIJF andEDIT steps must be run in one job.

4.4 Job Control Statsmnts

The list shown in Fif. 4.3 is an example of job control statements for FACOM/M380computer which is compatible with IBM 360, 370 series machines. The load module is pro-duced by compiling the FORTRAN subroutines together with the assembler routines. Theoverlay structure is described in Chapter 5.3. Two cataloged PDS files, PDSIN and PDSOUTshould be specified, which may have the same data set name. The contents of files are de-scribed in Chapter 6.

SLAROM: ACod«fefCl»Ho«otwttitfcnCtle»htionof Fut Rwctot JAERI12M

a. IGT - 1 (Sphere andIGT « 3 (Circular cylinder)

b. IGT -2 (Infinite slab)

unit cell

9

RXll)*O RX(K»

c. I G T - 4 (Square pillar) d. I G T - 5 {Two dimensional•quart pillar)

e. IGT - 6 (Hexagonal pillar) f. IGT « 7 (Two dimensionalhexagonal pillar)

na.4.1 AwiUbk otQ «MMtiyia PATH tt*p_.

JAERI1294 4. (MfcfixhpMEMiPnptntiMi

g. IGT - 8 (Square aMembly) h. IGT - 9 (Square assemblywith pin rods)

inihtCMOf IDIVP'O

m!hicaNoriDIVP>l

T

i

>

TTTT

"""1

<4

i i m

i. IGT - 10 (Annular assembly with regular arrays of pin rods)

IDIVP- 0

case N«4, NA-NPIM1 )«6

IDIVP-1

Fla.4.1 (eoetfaMd)

30 SLAftOM: A O>» fee (Ml HuBUiflwrtnt Crtwfcttai of F K Rfctoc JAEH12M

j . IGT - 11 (Annular assembly withasymmetric pin rods)

k. IGT-12(HaxagonalasNmblywithasymmetric pin rods)

case N-5, M-3NP-6

I. IGT-13 (xy two dimensional infinitt pillar)

TY17)TY(6)

TYC5I

TY(4)

TYI3>

TY(2)

TYI1)

21

16

11

6

1

22

17

(2

7

2

23

18

13

8

3

24

19

14

9

4

25

20

15

10

5

NX-5

NY-6

RX(1) RM2) RM3) RNW WORXW

m. IGT " 1 4 (Hexagonal assembly with concentric hexagonal arrays of pin rods)

RPPI2)RPP(3)

RXID-O

RX(4)

NX-3NTPIN«19NAPIN - 3NOPIN - 2IBETM -GOIDIVP « 1

Flt.4.1

JAERI12M 4. Guide for Iapot DM* Pnpintioa 31

Table 4.1 Total number of zones (NZ) for each geometry

IGT NZ

1.2,3,4,6

5,7

8

10

11,12

NX

2NX

NX»(NX+l)/2

NX»(NX+1) + N D p m , NAPIN* (NAPIN+ 1)

NAPIN » NDPIN jj

+ NAPIN • (IDIVF - ffiÊ) + NDPIN • ICP •>

NTPIN • NDPIN (*PjW + 1) + NX

+ NAPIN • (IDIVP - - ^ ^ ) + NDPIN • ICP •>

•) ICP- 0 if a pin rod doei not lie at the center.- 1 if a pin rod Uet at the center.

IGT«9

RPP(4>

RK(3) RW41 RX15I RXK) RXffl

N X - 6NAPIN-4N D P I N - 2I D I V P - 0

Example of region and materialnumber anignment for equare

Zoae NREG MAR ZOM NREG MAR

1 ~ 67~10

1112~I4

1516,17

1819

20,21222324252627

121212121345678

12121212I343434

2829303132333435363738394041

9101112131478

1112S634

34345634343434

Fif.4.2 Example of zone number.

SLAROM: A Code for CeU Homotenizatkm Olcnlation of Fist Reactor JAERI1294

• • JCLSNPL • •

//JCLO JOI/ / EXEC JCL«//SYS1N 00 0ATA,DLH»'**"// JUIER *14*2350,NA.NAKA(AIM,0431.110T.4 C.S W.2 1.5OPTP H0TIFY-J23SO,NStCLASt>R,PASII«>R0>

/ / EXEC L«0,LH.1JJ350.«L*ll0IC,PH«.Si.»«0«KJ/ / • • LOAD NODULE NAME//FT05F001 DD DSN>JO0OO.LHFIR.OATA<3AHPLl>,0ItP-SHR/ / « « SYSTEH INPUT DATA FILE • • •//PDSIH DD DSN'JOOOO.XSECTION.DATA,DISP»OLD/ / • • INPUT PDS FILE • • •//PDSOUT DD DSN-J000O.XSECTION.DATA,DISP»OLD/ / • • OUTPUT PDS FILE «••//FTO1FOO1 DD SPACE.<T«K,(70,K»>,umT.maO//FT02F001 DO SPACE-CTRK,(40,10>>,UNIT>VK10//FTO3FOO1 DO SPACE-<TRK,<70,10>>,UNIT>UK10//FT04F001 DD »PACE-(TRK,(*O,1O>>,UN1T.»K1O//FT0IF001 DO D3N-JO000.JFS3J2R.0ATA,DISP>SHP.,LAIEL-(,,,IN>/ / • • CNOtt SECTION I.URARr •««//FTOtFOOl 0D tPACE"(TRK,(400,JO>>,UNIT.|IK10//FT10F001 DO SPACE-<TRK,(70,10>),UN1T.«10//FT11F001 DD tPACE-CTRK,<40,10>>,UNIT«l«10//FT20F001 00 SPACE«(TRK,<40,10>),UNIT>tK10//FTJ1F001 DO SFACE"<T»K,UO,1C)>,UIIIT.»K1O//FT41F001 DO >PACE-<TltK,<r0,10>>,UNIT*W10//FT4JF001 DO *PACI-<TIIK /(«0,10>),UNIT>mi0//FTtJFOOl DD tPACE-<TP.K,C70,10>),UNlT«WIC10//FTS4F001 DO tPACF.-<T»K,(70,10>),UIIIT.KK10//FT53F001 DO >PACE-(TP,K,«OflO>),UNIT>MKio//FTItFOOl DO tPACE><TP.K,C(0>10>),UNIT>WIU0//FT71F001 DO DIN-J0000NAXt3PL3.DATA,DIIP'tHlt,LAIEL-(,,,III)/ / • • PL C»0»> SECTION LIMAP.V • • •

//FT72F001 DO SP»Ct-<T«K,<»0,10)),UNlT.W>;:0//FT7IF001 DD SPACEXTP.K, (40.10) I ,UNIT>HK10//FTI0F001 DO lP«Ct.(T«K,(40,10)),UNIT.KK10//FT90F001 DO tPACE><TP.K,(40,10>),UNlT.HK10

II

O0OOOO1O00000020000000300000004000000030000000*000000070

00000010

00000100

00000110OOOOOliO00000130000001400000013000000130000001*0000001*00000017000000110000001to00000>3000000140OOOOO23O00000230000002*00000027000000270

00000310000003100000031000000320000007*000000770

JCLSNPLJCLIHPLJCLSNPLJCLtNPLJCLSNPLJCLSNPLJCLSNPLJCLSHPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCiSNPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCLSHPLJCLSNPLJCLSNPLJCLtNPLJCLSNPLJCLSNPLJCLSNPLJCLSNPLJCLtNPLJCLtNPLJCLtNPLJCLSNPLJCLtNPLJCLtNPLJCLtNPL

•> SLNOVLYN ••

ENTRY

INSERTINSERTOVERLAYINSERTOVERLAYINSERTINSERTOVERLAYINSERTTNSERTOVtSLAYINSERTOVERLAYINSERTINSERTOVERLAYINSERTOVERLAYINSERTOVERLAYINSERTINSERTOVERLATINSERTOVERLAYINSERTOVERUtTINSERTINSERTOVERLAYINSERTOVERLAYINSERTOVERLATINSERTOVERL*'

OVERLATINSERT

SLARON

SLARON.CLEAPNCHS,REAG,RUPDSF#NATINVLEVEL2PCOL,OPNIUF,PREPDSLEVEL4PIJIN,FIJI,CHECK,INSERT,ELI"HAKETX , INSET7,ASCEND, VOLPIJLEVELSPATH.PAIN,PREPA,NAKEPT,CTL,HEX,HEX2.M.SMCOHPAR,DIVIDE,SLAa,HHHH,PATHHH,PREHH,tEONHHLEVEL5CLUP.CLIN,CEON,NAKETCLEVELSCLUP77,RDX1,GEOH7,HAKET,RPRINTL0CF.IPRINT,PREX7LEVELSCLUPN,CLIRH,HAKETH,SECT,INTRP,SEONHLEVELSPATHXY,PREKY,GEONXT,IPRTX,IPRTXPLEVEL4PIJ2.SIGRD,PAINT,DELT,TH0,ON(,FORHPINTH,ENX,FKINLEVEL2PIJF,INP1F,INP2F,INP3F,ITER,TEDITLEVEL2EDIT,EDITSLEVELiESLNJ,PREDIT,E,ALPHA,SETA,CLEAR,INPT,JAERI,SHIELDRSRCH,IXTERP,TY,IUHONOLEVEL2EINDLEVELSEINEO,EXPAND,SINPS,REGION,L«PSEN,RREIN1,RREINILEVELSSPD2,SVNPSII,JSERCH,KRGNLEVEL? .•SEARLEVELSREACTS,REACTN

NAHE SLARONHJ

OOOOOO1O00000020000000300000004000000030000000*00000007000000010

000000*0000001000000011000000120000001300000014000000150000001*00000017000000110000001*0000002000000021000000220000002300000024000000250000002*00000027000000210000002*0000003000000031000000320000003300000034000000350000003*00000037000000310000003*00000040000000410

SLNOVLYHSLHOVLYHSLMVLYHSLHOVLYHSLHOVLYHSLNOVLYHSLNOVLYHSLHOVLYHSLHOVLYHSLNOVLYHSLNOVLYHSLHOVLYHSLNOVLYHSLHOVLYHSLNOV.'.YHSLHOVLTHSLNOVLTHSLNOVLYHSLHOVLTHSLNOVLYHSLNOVLYHSLHOVLYHSLHOVLYHSLNOVLYHSLNOVLYHSLNOVLTHSLNOVLYHSLNOVLTHSLNOVLTHSLNOVLYHSLNOVLTHSLNOVLYHSLNOVLYHSLHOVLYHSLHOVLTHSLHOVLTHSLHOVLTHSLNOVLTHSLHOVLTHSLHOVLTHSLHOVLTHSLHOVLTH

JAERI1294

5. Structure of SLAROM

5.1 Calculation Flow

1) PREPThe calculation in SLAROM consists of five steps, PREP, PATH, PIJF, EDIT, EIND and

RATE. The calculation procedure is briefly described below. The PREP reads input data anda cross section library, then prepare the region dependent effective cross sections. The flow isillustrated in Fig. 5.1. The effective microscopic cross sections are calculated based on themethod described in Chapter 3.2. The cross sections of homogeneous medium are edited onthe PDS file if ANAME is not blank. The effective cross sections for each material are writtenon scratch files to be used in the latter steps. If the option for critcal buckling search (IBSW)is equal to 2, the critical search is carried out for the homogenized medium and the bucklingvalue is printed out. This value is used as an initial guess of the critical search for the hetero-geneous cell. The DB* term is calculated for the homogenized medium using the searched orthe input values of B* and added to all the region cross sections of total, transport and absorp-tion.

2) PATHIn PATH step, the collision probabilities are calculated and written on units 20 and 21

which are used in PIJF and EDIT steps. The calculation flow is illustrated in Fig. 5.2. At first,the geometrical path table is produced in the subroutines PATH, CLUP77, CLUP, CLUPHPATHXY and PATHHH, then the isotropic and anisotropic collision probabilities are com-puted using the analytic function or the tabulated Bickly function. These probabilities arenormalized to unity and divided by the total or the transport cross sections if necessary to beused in the calculations of diffusion coefficients.

3) PIJFIn this step, the multi-group equation Eq. (2.10) is solved and the cell averaged values

of reaction rates and cross sections are calculated by weighting with the fine structure flux.The calculation flow is illustrated in Fig. 5.3. At first the input data for this step, cross sectionsand collision probabilities are read in the subroutines INP1F~INP3F. Using the initial fluxguess, the fission source terms are calculated and the flux distribution in the cell is obtainedby the matrix inversion method from the highest to the lowest energy groups. The slowingdown source is obtained from the flux of higher energy groups calculated already. The multi-plication factor is computed using all the group fluxes and the convergence test is performed.The convergence criteria for a reaction rate are given by users.

This outer iteration continues until the convergence criteria are satisfied. If the bucklingsearch is necessary, the multiplication factor is compared with unity. When the difference issmaller than 0.001, the iteration terminates, otherwise the buckling search continues. In thelatter case, a control returns to the main program and it calls the subroutine BSEAR. Aftera new value of buckling is determined by an extrapolation, the DB* term is modified andwritten on the scratch files. The main routine resets the value of IBSW and calls PATH again.The new collision probabilities are calculated again in PATH, and PIJF step is carried out.Such an iteration loop is automatically controlled until the critical search is converged. The

34 SLAROM: A Code for CeU HomofRdutloa CricuUtka of Fist Reactor JAERI12M

ClPBOB'PREP)

IESUJJII Rood \m dato |——( |

I Rwd JFS3 Upt library ona wrltt on JAER

Mkrary tram JAER(T« OtiWlOHMDactff ctrnctlM.

Critical buckltot of InwoowtwitPut tffKlht crow ncHww of howwwiwow

EffKtlW HMCfO»CO»tC CWM

Dancotf factor for «lob I I Oancotf foctof for cvHndtfI

1 CALL JAERI

PREMT

)»lc crow swtiMiandOB* MmcttM

Wrilt •ftacllra crow stctlom of «Kh n i i M M LIBR

j Put wocroicoolc crow stctlom of r>§ion>

PCS

FJf.5.1 Cilcul»tion flow of PREP ttep.

JAERI1294 S. Structure of SLAROM

QPROB'PHTH)

I

C3-

CtlcuUtion flow of PATH ft«p.

cell averaged values of reaction rates and macroscopic cross section for all the groups areprinted out together with the collapsed one group values. Note that these values include thecorrection term for£>B*.

4) EDITThe subroutine EDIT reads input data required in this step and sets the array of variables,

then calls EDITS. In the subroutine EDITS, various cell averaged cross sections to be editedare calculated by using the region dependent cross section, the neutron flux and the collisionprobability which are read from the scratch files. The calculation flow is shown in Fig. 5.4.At fust, the anisotropic diffusion coefficients are computed basing on Eqs. (3.17) ~ (3.21).

36 SLAROM: A Code for Cell Homo* m Calculation of Fut KMCtot JAERI1294

(IPROB'PIJF)

I

Summation of fMWonsource, noriMKzaNon

CALL INPIFINP2FIHP3F

St l ntw Nurc* form

Sohifkm of matrix equation

Slowing down town

IBSW-9999Print fkid tlfMNlvtbucklint

Riod eoWikm pnk«Mlity

Print fhiK

flw and iMctlM rdt

rnm CM IVtrafN IWCHM flN

Mm it iKl«M hi £•

Extrapotatotion of B*

Print mformotion of critico) scotch

Modify crow Mctions with U M

of ntw wkit of B*

Writt cross stction

[IBSW'1011

(IPRBi » PATH)

The B* term is subtracted after this procew. The eel i opk crou sections andfission spectrum are computed basing on Eqs. (3.9) — (3.15) and those of Pi component ofscattering matrix are also obtained if IPL>0. The calculated cross sections are written on thePDS file if ANAME is specified. The cef aiasaniii •Mcroaoopic cross sections are computedbasing on Eqs. (3.22) ~ (3.31) if If KXXJT+0- For the case WCED > 0, the cross sections onunit 3 are reordered and written on unit 54 for a convenience of execution. If MICOUT < 0 ,the neutron balance by materials are calculated, and the total production, fission and absorp-tion rates and the leakage rate are edited. The leakage rate is estimated from the DB*+ termwhere D is the isotropic diffusion coefficient. The EDIT step can be repeatedly run. Forexample, when the cell calculation is performed for a multi-drawer model in the PREP ~ PIJFsteps, the averaged cross sections of each unit drawer can be edited by running only the EDITstep repeatedly in which each sub-cell region is assigned in the input data.

JAEM1294 5. Structure of SLAROM

(IPBM'EPIT)

IStt

| R i d ttw .DBF, I t ond Pi) | —

Cotc«Wt aid print* totropfc and »4totiopicdiffwion ootffieimtt

RNd Z•

CriiwiSaklracl

, |

HdnOB*

-—uHtm

tc craw ttctimt

JSL.

\m HHrtrfX Of PI QMUBWt]

no| Put crott nctiow and ftwton tptclram on PDS

PDS

Fit. 5.4 Cdcubtion flow of EDIT «t«p.

SLAKOM: ACo*«foc<MlHn«nn«lfiHnnC«lcal«tioiiof Ftrt R»»ctoc JAEM12M

M M iiTii M nvm§r nom of cm MCIWM W M

Rwd ID infornation

Sat array

PDS

inctlt

nf im dtpmtfml CRM MCIIOM

and pomr dMribNtiont)

Print fiwlts

Cakulat* toM iMction by using CMI avtrog«d

CIOK MCtiOM

Print rtNHs

IMMMI

Fif. S3 C*»Utton flow of RATE Hep.

5) RATEThe calculation flow of RATE step is illustrated in Fig. 5.5. In this block, the micro-

scopic cross sections are necessary, so users should set MICOUT # 0 in the input data forPREP. The neutron flux is read from unit 4 and the microscopic cross sections are from unit 3 .The reaction rate is calculated for each region by using the region dependent microscopic crosssections which have been obtained basing on Eq. (3.3) for heavy nuclides. The cell averagedmicroscopic cross sections which are read from the PDS file are also used to calculate the totalreaction rate over the cell. For each nuclide, the groupwise reaction rates are calculated andedited, then the total reaction rates sumed over the groups are edited.

6) EINDThe subroutine EIND reads input data and sets the arrays. The subroutine EINED which

solves a one dimensional diffusion equation and the perturbation calculation routine SPD2 are

JAERI1294 5. StoKtanorSLAROH

|Rood fMan mOtmUm PCSfr' ' 1|R*o< ttwfew iptcmwi ftmTcinT]

R*dd IwckHM (Mt if mcmiifi I - /~~\

Cofwctiow of DB1 Wm\I

If MUPSEiO , MIIC'OPut Xi

Fif-t^S CdMktkMflowofEINDitep.

called from EIND. The calculation flow is illustrated in Fig. 5.6. The cross sections and fissionspectrum are read from the PDS tile and the DB2 term is corrected for the absorption andtotal removal cross sections. The normal and adjoint flux are obtained in the subroutineEXPAND and stored on unit 80. If LAPSE > 0 , the group collapsing routine LASPEM iscalled. The macroscopic and/or microscopic cross sections are collapsed into the broad groupstructure with use of Eqs. (3.33) ~ (3.39). If If LAPSE > 0, another sets of cross sections are

40 SLAKOM: A C o * tot Ot IItiMO|«*iti<» CUcul»tfc» of Fut R—ctoc JAEM12K

R«ommPill

d ni nID

pOfl MffiMT

MMT MM

NnonMtion

of flw

of aw

tok* \mt

• MCtKMttOkt C*t*Md

CCALL UPSEM>

tCALL RREIN l>

I Writ* crow wctloni fcr tofword whrtlonl

I NPERT • NPEffTt <

Rood iMmbtr nonw for pirhirbQiion cokutalionGtt craw MctiontWrita am NdiOM on unit 3 >NPERT • NPERT + 1

Flf. 6.« (continued)

JAEM1M4 5. StnetanoTSLAItOll 41

also collapsed by using the neutron flux of the region auigned in the input data. The col-lapsed broad group cross sections are saved on the PDS file with the member names assignedby the input data.

The reaction rate distributions can be calculated in the RREIN 1 and 2 routines. IfNPERT > 0, the first order perturbation calculations are carried out. The parameter NPERTis a number of cases to be calculated. The perturbed cross sections are read for all the casesand written on unit 3. The subroutine SPD2 calculates the reactivity worths for NPERT cases.The reactivity worths are printed, out at each mesh point and region, and for the groups.

5.2 Function of Subroutint

The main function of subroutines is described below.The library function in FACOM-M380 is omitted.

1. ALPHA (function)Interpolates shielding factors by using a hyperbolic function.Called by SHIELD

2. BETA (function)Interpolates or extrapolates shielding factors by using a hyperbolic function. Thesubroutines ALPHA and BETA are used properly according to the type of f-table.Called by SHIELD

3. BLOCKD (KIDATA)Block data of quadratic interpolation coefficients used in the calculation of Kim function.

4. BSEARCalculates a modified value of budding and prints an information of buckling search. Byusing a new value of B*, the total, transport and absorption cross sections are modified.Called by MAINCalls FLIN (statement function)

5. BUHOMOCalculates a critical budding for homogeneously mixed material. This is used as an initialguess of buckling search.CaUedbyPREDITCalls FLIN (statement function)

6. CHECKPerforms a check of input geometry.Called by PIJIN

7. CHIMIXMixes the fission spectrum by weighting with atomic number densities. Fission spectrumof »SU, "•U and M*Pu can be selected.Called by INPT

8. CLEA and CLEARSets variables to be a constant value.

9. CLINPrepares geometrical data of annular cluster.Called by CLUP

10. CLINHPrepares geometrical data of hexagonal cluster.Called by CLUPH

11. CLUP

, m JAEKI12M

Called by PIJINCalls CLIN,MAKET

12. CLUPHSets arrays.Called by PIJINCalls CLINH.MAKETH

13. CLUP77Sets parameters and arrays used in square cluster calculation. ,.CaUedbyPIJINCalls RDX1, PREX7, MAKET

14. COMPARSets parameters used in DIVIDE.Called by HEX2, SQ2Calls AMAX1, AMIN1, DIVIDE

15. CYLComputes path length in cylindrical geometry.Called by MAKEPTCalls INSERT

16. CYLNDFCalculates Dancoff factor in pin geometry.Called by INPUT

17. DELTIntegrates Kt function and computes collision probability for pin cell. If an optical pathlength is very small, an approximate formula is used.Called by PAINT, PINTH

18. DIVIDEObtains crossing points of a flight line and an azumuthal boundary of region.Called by COMPAR, SQ2

19. E (function)Calculates £. function of order 1 ~ 5.Called by SLABDF

20. EDITPrints input data of EDIT section and sets arrays used in EDITS routine.Called by MAINCalls REAG, EDITS

21. EDITSComputes cell averaged cross sections and directional diffusion coefficients. Macroscopiccross sections are printed and/or written on PDS file. Microscopic cross sections arewritten on PDS file by an option.Called by EDITCalls REAG, CLEA, PRTMAC, PUTIDX, PUTMAC, PUTKAI, PUTMIC

22. EINDReads and prints input data for EIND section, and sets arrays for diffusion calculation.Called by MAINCalls REAM, EINED, SPD2

23. EINEDReads and writes input data for diffusion calculation. Macroscopic cross sections are readfrom PDS file and collopased macroscopic- and microscopic cross sections, and flux a n

JAERI1294 5. Stnctwtof SLAKOM 45

saved on PDS file. An interface file is prepared for adjoint and perturbation calculations.Called by EINDCalls CLEA, REAM, GETKAI, NAMSET, PDSLEN, GET1DX, GETMAC, EXPAND,

REGION, PUTKAI, PUTFLX, LAPXAI, LAPENG, MAXO, PUTIDX, LAPSEM,RREIN1

24. ELIMPrepares region identification numbers and path length of each region along the flightline. c:CaUed by MAKEPT, M AKET, MAKETH, MAKETC

25. ENX (function)Computes EiH(x) function.CaUed by ONE, TWO

26. ESLMJReads and writes input data for PREP section, and sets arrays used in the calculation ofeffective cross sections.CaUed by MAINCall! REAM, RDJFS2, RDJFS3, INPUT

27. EXPANDSolves one dimensional diffusion equation and computes an eigenvalue.Called by EINEDCalls REGION, SIMPS

28. FK1N (function)Bickley function is computed basing on the quadratic interpolation formula with use ofthe tabulated coefficients.Called by ONE, TWO

29. FORMComputes the collision probability based on the reciprocity relation, and then normalizesit. Isotropic and directional collision probabilities are edited on a line printer or a scratchfile.CaUed by PAINT, P1NTH

30. GEOMComputes path length for the case of annular cluster.Called by MAKETCCalls INSERT

31. GEOMHComputes path length for the case of hexagonal duster.Called by MAKETHCalls SECT, INSERT, INTRP

32. GEOM7Computes path length for the case of square cluster.Called by MAKETCalls LOCF, INSET7

33. HEXComputes path length for the case of hexagonal lattice of pin without azimu J- J division.Called by MAKEPTCalls INSERT

34. HEX2Computes path length for the case of hexagonal lattice of pin with azimuthal division.

SLAKOM: ft f u l l fill f i M I I i i M i u M f r i l i n f i l l i h l i i w nf T u l n i l III J A E M 1 2 M

Called by MAKEPTCalls INSERT, COMPAR

35. HOMOXSComputes macroscopic effecthre cross sections for homogeneous mixture and edits themon PDS file.Called by INPTCalls CLEA, PRTMAC, PUTIDX, PUTMAC, PUTKAI, PUTMIC

36. INPTReads and writes input data for PREP section and sets arrays used in the cslculation ofeffective cross sections of each region.Called by ESLMJCalls REAM, CHIMIX, JAER1, KINFHM, HOMOXS, SLABDF, CYLNDF, PREDIT

37. INP1FReads and writes input data for PIJF section.Called by PI JFCaUs REAM, REAI

38. INP2FReads cross sections from a scratch file or cards.Called by PIJF

39. INP3FReads collision probability, flux guess and source density.Called by PIJFCalls REAG, REAM

40. INSERTSearches crossing points of a flight line and a region boundary.Called by CYL, HEX, HEX2, SQ, SQ2, GEOM, GEOMH

41. INSET7Searches crossing points of a flight line and a region boundary for square cluster geometry.Called by GEOM7

42. INTRPCalled by GEOM7

43. IPRINTPrints zone, region and material numbers in the duster map.Called by PREX7

44. ITERPerforms fission source iterations for multi-group integral transport equations.Called by PIJFCalls MATINV

45. IXTERPInterpolates or extrapolates the values of «» corresponding to R value.Called by RSRCHCalbYY

46. JAERIReads library tape of group constants set and computes effective cross sections by usingself-shielding factors.CalledbylNPTCalls CLEA, SPLINE, SHIELD

47. JSERCH

JAEKI1294 5. Stnwtowof SLAROM 46

Searches the mesh point at region boundaries.Called by SPD2

48. KINFHMComputes an eigenvalue of infinite homogeneous medium by taking account of pseudoabsorption term.Called by INPTCalls CLEA

49. KRGNObtains mesh point numbers at the region boundary.Called by SPD2

50. LAPSEMWrites collapsed cross sections on PDS file.Called by EINEDCalls NAMSET, PDSLEN, GETKAI, LAPXAI, PUTKAI, GETMAC, LAPXS, LAPMX,

LAPPL, PUTMAC, GETMIC, PUTMIC51. LIBRD2

Reads library cross sections of the JFS2 type.Called by RDJFS2Calls CLEA, REAI

52. UBRD3Reads library cross sections of the JFS3 type.Called by RDJFS3

53. LOCF (function)Specifies a zone number at an arbitrary mesh point.Called by GE0M7, PREX7, RPRINT

54. MAIN (element name SLAROM)Main program of SLAROM.Calls ESLMJ, PCOL, PIJF, BSEAR, EDIT, EIND, REACTM

55. MAKEPT

; Makes a path table in order to calculate the collision probability for slab and pin geom-i etry.I Called by PATH! Calls OPNBUF, SLAB, CYL, SQ, SQ2, HEX, HEX2, EUM, WRTBUF, CLSBUF, RDBUF! 56. MAKETj Makes a path table in order to calculate the collision probability for square geometry.

Called by CLUP77Calls OPNBUF, GEOM7, ELIM, WRTBUF, CLSBUF, RDBUF

57. MAKETCMakes a path table in order to calculate the collision probability for annular cluster.Called by CLUPCalls OPNBUF, GEOM, ELIM, WRTBUF, CLSBUF, RDBUF

58. MAKETHMakes a path table in order to calculate the collison probability for hexagonal cluster.Called by CLUPHCalls OPNBUF, GEOMH, ELIM, WRTBUF, CLSBUF, RDBUF

59. MATINVComputes inverse and determinant of matrix equation. The solution of the integraltranspo; > equation is obtained in this routine.

46 SLAROM: A Code for CeUHomofeniziOonOlcuUtior of F«t Reactor JAERI1294

Called by ITER.PAEDT60. ONE

Defines the function, Ein(x) , h\(.x) and EXP(x) of order 2 and 5 to calculate the col-lision probability.Called by PAINTCalls ENX, FKIN

61. OPNBUFReads/writes the path vector on a scratch unit with fixed record length using the buffer.Entry: OPNBUF, WRTBUF, CLSBUF, RDUFCalled by MAKEPT, MAKET, MAKETH, MAKETC, PAINT, PINTH

62. PAINReads and writes input data for PATH section.Called by PATH

63. PAINTComputes the collision probability for plate cell.Called by PIJ2Calls OPNBUF, RDJJUF, DELT, TWO, ONE, FORM

64. PATHSets arrays used in the calculation of collision probability for slab and pin geometry.Called by PIJINCalls PAIN, PREPA, MAKEPT

65. PCOLReads input data for PATH section and sets parameters.Called by MAINCalls REAM, REAI, PIJIN, PREPDS, PIJ2

66. PIJFControls the calculation flow of the neutron flux and eigenvalue, and sets arrays.Called by MAINCalls INP1F, INP2F, INP3F, ITER, TEDIT, INP2FZ

67. PIJINReads and prints input data for PATH section, and sets arrays used in the path tablecalculation.CaUed by PCOLCalls REAI, REAM, PIJ1, CHECK, PATH, CLUP77, CLUP, CLUPH

68. PIJ1Reads and prints geometrical input data.Called by PIJINCalls REAI, REAG

69. PIJ2Sets arrays for the collision probability calculation.Called by PCOLCalls SIGRD, PAINT, PINTH

70. PINTHControls the calculation flow of collision probability.Called by PIJ2Calls OPNBUF, RDBUF, DELT, FORM

71. PNCHSWrites and punches neutron flux.

JAERI1294 5. Structure of SLAROM 47

CaUed by TEDIT72. PREDIT

Makes macroscopic cross sections of each material region and writes on a scratch file.If an option of Pi component is chosen, the Pi library is read in.CaUed by INPTCalls BUHOMO, CLEA

73. PREPAReads input data for PATH section and constants used in the collision probability cal-culation.CaUed by PATHCalls FUN, CLEA

74. PREPDSReads fission spectrum, cross sections from PDS file which are used in PATH step.CaUed by PCOLCalls CLEA, REAG, GETKAI, GETIDX, GETMAC

75. PREX7Computes volumes of zone and mesh, and edits maps for square cluster geometry.Called by CLUP77Calls LOCF, IPRINT

76. RDJF2Sets arrays used in reading the group constants set of JFS2 type.Called by ESLMJCalls LIBRD2

77. RDJF3Sets arrays used in reading the group constants set of JFS3 type.CaUed by ESLMJCalls LIBRD3

78. RDX1Checks the geometrical data.CaUed by CLUP77

79. REACTMReads input data for RECT section and sets arrays.CaUed by MAINCalls GETIDX, REACTS

80. REACTSComputes reaction rate distribution in cell.CaUed by REACTMCalls GETMIC

81. REAGReads data in free format. This routine has two entries, REAI and REAM.CaUed by EDIT, EDITS, INP3F, PAEDT, PREPA, PIJl, PREPDSCalls IBCD

82. REGIONObtains mesh point numbers at the region boundaries.Called by EINED, EXPAND, RREIN1, RREIN2, SIMPS

83. RREIN1Reads input data for the calculation of reaction rate distributions and sets arrays.CaUed by EINED

48 SLAROM: ACode foiCMlHomopniMtion CalcuUtioiiorFut Retctor JAERI1294

CaUs REAM, REGION, RREIN284. RREIN2

Computes reaction rate distributions by using neutron flux obtained in the one dimen-sional diffusion calculation.Called by RREIN1Calls CLEA, REGION, GETIDX, GETMIC

85. RSRCHPerforms a R-parameter search of shielding factors if the group constants set has a depen-dence on R-parameter.Called by SHIELD, SPLINECalls IXTERP

86. SHIELDComputes self-shielding factors by using a hyperbolic function.Called by JAERICells RSRCH, ALPHA, BETA

87. SIGRDReads cross sections from unit 11.Called by PIJ2

88. SIMPS (function)Integration of point-wise data basing on Simpson's formula.Called by EXPANDCalls REGION

89. SLABComputes path length in slab geometry.Called by MAKEPT

90. SLABDFComputes Dancoff factor for plate cell basing on Meneghetti's formula. E, function isused.Called by INPUTCalls CLEA, E

91. SPD2First order perturbation calculation with use of real and adjoint fluxes obtained byone dimensional diffusion calculation. This subroutine is modified from the SIMPLE-Dcode19'.Called by EINDCalls KRGN, JSERCH, SYMPSN

92. SPLINEInterpolates self-shielding factor by using Spline function. If JFS3 type library is used,this subroutine is called.Called by JAERICalls INSPL, RSRCH

93. SQComputes path length for the case of square lattice of pin without azimuthal division.Called by MAKEPTCalls INSRT

94. SQ2Computes path length for the case of square lattice of pin with azimuthal division.Called by MAKEPT

JAERI1294 S. Structure of SLAROM 49

Calls INSERT, COMPAR95. SYMPSN (function)

Integration by Simpson formula.Called by SPD2

96. TEDITPrints output results obtained in PIJF step. They are neutron flux, cell averaged valuesof diffusion coefficients and macroscopic cross sections and total reactions rates.Called by PIJFCalls PNCHS, REAI, REAM

97. TWODefines a function, £,«(*), &„(«) and EXP(x) of order 3 and 5 to calculate the colli-sion probability.Called by PAINTCalls ENX,FKIN,EXP

98. YY (function)Function for a linear interpolation.Called by IXTERP

99. Utility subroutines for PDS fileMany utility subroutines have been developed in order to access the PDS file effectively

and to simplify the program structure. These routines can be easily applied to make auxiliaryprograms. The subroutine names and their functions are briefly described below. Entry namesare shown after a slash (/).

(1) GETBSQ/PUTBSQ/FNDBSQRead / Write / Get length of words for buckling values.

(2) GETFLX/PUTFLX/FNDFLXRead / Write / Get length of words for neutron flux.

(3) GETKAI/PUTKAI/FNDKAIRead / Write / Get length of words for fission spectrum.

(4) GETMAC/PUTMAC/FNDMACRead / Write / Get length of words for macroscopic cross section.

(5) GETMIC/PUTMIC/FNDMICRead / Write / Get length of words for microscopic cross section.

(6) MSG.MSGPRPrint of message.

(7) NAMSETComposes a member name of 8 letters from ANAME (6 letters given by input data) andNMPROG (program name) according to the rule mentioned later.

(8) NMCHECChecks a member name and replaces a blank or an undefined letter by a symbol ¥($) .

(9) PDSERRPrints an error message if an I/O error is detected in accessing the PDS file.

(10) PDSGET/PDSPUT/PDSREN/PDSDEL/PDSLENRead/ Write/Rename/Delete/Get length/for the PDS file. This routine calk RWPDSFwritten in an assembler language. A new program utilizing the I/O function of PDS filecan be made by installing these subroutines.

(11) PRTBSQPrints buckling values.

(12) PRTFLX

50 SLAROM: A Code for Cdl HomotMifc»tk)» Ctlcutottoa of Fi»t KmcUx IAEM12M

Prints neutron flux.(13) PRHDX

Prints ID information.(14) PRTKAI

Prints fission spectrum.(15) PRTMAC

Prints macroscopic cross section.(16) PUTIDX/GETIDX

Read / Write ID information on the PDS file.

5.3 Program T I M of SLAROM

MAIN

ESLM> PCOL PIJF BSEAR EDIT EIND REACTM

PLIN

REAM RDJFS2

UBRD2

REAI

PRTMAC

POT —

PUTMAC—

PUTKAI —

PUTMIC—

RDJFS3

UBRD3

MPT

—REAM

—CHftHX

— JAER!

HOMOXS —

-PREDTT

SPLINE

—KINFHM

—SLABDF

U—CYLNDF

INSPL

—RSERCH

IXTERP YY

-SHIELD

BUHOMO

FUN

-RSRCH

IXTERP

—ALPHA

— K T A

JAEU1294 S. Structure of SLAKOM 51

REAM PREPDS

— REAG

— GETKAI

— GETIDX

— GETMAC

INP1F INP2F

—REAM

'—REAG

INP3F HER

h-REAG IMATINV

1—REAM

TENT MP2FZ

— PNCHS

— REAI

— REAM

REAM REAI REAG EDITS

— REAG

— REAM

—PRTMAC

—FUTIDX

—PUTMAC

—PUTKA1

—POTMIC

SLAJtOM: M E U 1 3 M

REAM EINED

-REAM

-GETKAI

—NAMSET

-IDSLEN

— GETIDX

— GETIIAC

— EXPAND

— REGION

I—SIMPS REGION

-REGION

•PUTKAI

-PUTFLX

-LAPENG

-PUTIDX

•RREIN11—LAPSEM- NAMSET

—PDSLEN

— GETKAI

— LAPXAI

PUTKAI

— GETMAC

— LAPXS

— LAPMX

— LAPPL

—FUTMAC

—GETMIC

—PUTM1C

SPD2

— KRGN

— JSERCH

— SYMKN

GETIDX REACTS

GETMIC

JAEM12M

PAIN PREPA MAKEPT

I IOPNBUF SLAB

WRTBUF

CLSBUF

RDBUF

ICYL

ISQ

INSERT

ISQ2

IHEX

IHEX2

IBUM

DIVIDE I IINSERT COMPAR

DIVIDE

RDX1 PREX7

tLOCF

IPRINT

MAKET

—OPNBUF

— GEOM7—1—

— ELM '

— GEOM7-

ELOi

— WRTBUF

—CLSBUF

— RDBUF

LOCF

INSET7

rCLIN

OPNBUFi

MAKETC

GEMO

INSERT

EUM WRTBUF

CLSBUF

RDBUF

PREXYI

1PRTX

MAKETX

GEOMXY

CUNH

SECT

MAKETH

II I I

OPNBUF GEOMH BUM

T 1DJSETR IHTRP

WRTBUF

CLStUF

PREHH

GBOMHH

INSERT

MAKETX

GBOM7

INSET7

VDLPU

ELM

M SLAKOM: ACmkforCMHoaofMtatlMCUcaktioaof FfetKMctor JAERI12M

6. Fite Roqummwit

SLAROM uses four types of files, input and output PDS, cross section tibnty, systemI/O and scratch files. The following describes the contents of these files.

6.1 PDSFito

The PDS (Partitioned Data Set) file"> is a direct access file written in binary mode, ofwhich DD name is assigned in the program. Users should allocate the data set as a PO fieprior to running SLAROM. A typical DCB parameters are as follows;

RECFM-U, LRECL-O, BLKSIZE-900.

SLAROM outputs the data on the file with DDNAME - PDSOUT and reads from the onewith DDNAME * PDSIN. Usually, these two flies have the same data tst name. Each datablock saved in the file b refered by a member name defined by eight letters of alphabetical(A ~ Z) and numeral (0 - 9) characters, and other special symbols. Among of them, the firstsix letters are assigned by users and the last two are automatically assigned in the code. Whenthe cross section data are saved, ID data are also created and saved. The ID data containsgeneral information concerning the saved data.

(1) How todsThe member name is defined according to the following rule.

° 1st ~ 6th letters: The variable ANAME is assigned, which is input by users. If the lengthof ANAME is shorter than six or ANAME includes blanks, the symbol ¥ ( $ ) is iaaartsdthere by the code.

° 7th letter: This letter presents the program name. For the data produced by SLAROM,'S' is used,

o 8th letter: It identifies a kind of data and is set by the code.The special symbols are used as shown in Table 6.1. The symbol ¥ ($) , for example, isused to present the macroscopic cross section. For the microscopic cross section, thesymbol shown in Tabte 6.2 is sequentially assigned to every nuchde in the order accordingto input data. If users need not save the data, enter blanks for ANAME.Example of member nameIf the input data is as follows;

ANAME -SAMPL1,

MICOUT * 3 and MELM ' 925,928,949,

the member names saved in the PDS file are

ID SAMPL1SO,macroscopic cross section SAMPL1SV,fission spectrum SAMPL1S#,(The fission spectrum is alway saved.)

The member names for the microscopic cross sections of each nudide depend on the sequenceof input code numbers.

JAEM1294

TaMe C.1 Symbol to identify thecontort of data in PDSfile

Content Symbol

ID 0Macroicopic croei section ¥ ($)Budding «Fiteioo tpectnun #Neutron flux Z

TabJefc2 Symbol to identify nuclide for micraecopic

Sequence

1234S

6789

101112

croei section in FDS file

Symbol

123456789ABC

Sequence

1314IS1617

18192021222324

Symbol

DEFGH

IJKLMNO

Sequence

2526272829

3031323334

Symbol

PQItST

IIV

wXY

If MELM - 92?, 928,949, the member names are

925928949

SAMPLS1,SAMPLS2,SAMPLS2.

If MELM * 949,925,928, the member names are

949925928

SAMPLS1,SAMPLS2,SAMPLS3.

If MICOUT<0, all the nuclide* are saved with the member name of which 8th letter isdetermined according to the order appeared in the data NCODE. When the member name isinput to read the data from the PDS file it is sufficient to punch the first six letters. The lasttwo letters are internally set. In the case of sample shown above, the member name SAMPL1is input.

(2) Physical content of data sared in PDS fifeThe data written in/or read from the PDS file have the following physical content.

1. ID (control information)

Title (18)MAXGIDSIPLMAXMMAXINMICNMICRO(NMIC)NUCNNMNUC(NUCN)DENHM(NUCN)DATEENERG(MAXG+1)

Arbitrary letten up to 72 columns.Maximum number of energy group.Maximum slowing down group including self-group sck- .«.Order of Legendre expansion for scattering.Length of nucroscopk cross sections (words).Length of microscopic cross sections (words).Number of nucMdes saved m the file.Code number of nucHdes.Number of nucUdes constituting macroscopic cross sections.Code number of NUCN nucBdes.Atomic number density (10** atom/cm3 unit) of NUCN nudides.Data of production.Energy boundaries of groups.

SS SLAROM: AQ«l»forCMHo«oi«*»Uo«Ok»l»tk«o.-F»»tRMCtot JAEM12M

2. Macroscopic cross sectionThe following cross sections are included with a repetition of energy groups.

S « . " E / . D,,, D±, Df, 2rr. Eft £ / ,

S, g-i(.j=g, g+U g+IDS-l),

E../.«-/O=*. *+l. g+IDS-lh 1=1. IPD

Note that the up-scattering is not considered.3. Microscopic cross section

The following cross sections are included with a repetition of energy groups.

o,, vof, otr, a/, a,, Oim, On,I,, ft, Dn. Oe, o, (dummy),

o*,ri( 3 =g. *+l. g+IDS-lX

o,,i.i-i<U=g.g + l, g+IDS-1), 1 = 1, IPD

Undefined cross section is sets to be 0.4. Fission spectrum

X*. (.g=l. MAXG).

5. Buckling values

BSO«, Ut = l. MAXG).

6. Neutron flux or adjoint flux

Pm*. ( f = l . MAXG).

(3) Error code for PDS I/O operationIf an error operation is encountered in I/O access, the following messages are printed out.

Users should confirm the member name or the error code ECODE.

ECODE Explanation

1 File open error. The file is improperly assigned or is nonexistent.2 Write (create new member) operation is specified but the member is

already existent.3 Member is nonexistent for this operation.4 Error in list operation.5 Specified words length of this read operation is greater than the length

of member.6 Lengths of data are mismatching.7 Reserved.9 Error in write operation.

10 Error in read operation.11 Error in member registoration or deletion operation. Check the vacancy

area for directory.

6.2 Cross Section Ubrary Fit*

The cross section library is read from logical units 8 and 71 which is written in binarymode. The contents of records are described below for the JFS3J) and JFS22> type libraries.

JAEU1294 t. FUHtylnmmta ST

(1) JFS-3 library Format (binary)#1 LNMAX, IMAX, MXCHI, MXR1D, MTXR23, MXDNSE, MXDNSI, MXDNS2,

MXDWNE, MXDWNI, MXDWN2, MXRFAC, MXSIGO, MXTEMP, MXR, ISWHLNMAX ; no.ofnuclideIMAX ; no. of energy groupMXCHI ; no. of fission spectrum setMXR1D ; no. of reaction in l -Ddata---8: /»v.c ,m, «/. ft. «r, n2*MTXR23 ; inelastic matrix data specification

(MTXR23 • 2—inelastic and («. 2K ) daU are given)MXDNSE ; max (LD(1,M ), * « 1 , LNMAX) except for hydrogenMXDNSI ; max (LD(2,« ), » « 1 , LNMAX)MXDNS2 ; max (LD(3, x ), » - 1 , LNMAX)MXDWNE ; max (LA(1,» ), * * 1, LNMAX)MXDWNI ; max (LA(2, ir), n - l , LNMAX)MXDWN2 ; max (LA(3, n), * - 1, LNMAX)MXREAC ; no. of reaction in F-table - - - 6: / , c. W, r, #r, mMXSIGO ; no. of a, -valuesMXTEMP ; maximum no. of temperature!MXR ; maximum no. of R-valuesISWH ; position of hydrogen - - - if ISWH « 0, no hydrogen data.

#2 NCODEULNMAX), ENBNDdMAX+1), CHIQMAXJMXCHI), NCODXQtfXCHI),AW(LNMAX), LD(3,LNMAX), LA(3,LNMAX), MSF(MXREAC,LNMAX), TAB(MXSIGO.LNMAX)

NCODEL ; nucUde code numberENBND ; energy boundary (ev)CHI ; fission spectrumNCODX ; nucUde code number which gives fission spectrumAW ; atomic weight in a.m.uLD ; maximum sink group number-•-l:elastic 2:inelastic 3:(n, 2n)LA ; lowest energy group that the cross secions are given — suffix is

the same as LD.MSF ; f-table specification - • • if MSF»0, f-table does not exist.

— -if MSFÔ, MFS is no. of temperature.TAB ; o,-values

#3 FT(MXTEMP,LNMAX), RPARAM(MXSIGO,MXR,LNMAX), NTEMP(MXREAC,LNMAX), NR(MXREAC,LNMAX)

Pi ; temperatureRPARAM ; R-valueNTEMP ; highest energy group that temperature-dependence exists, other-

wise NTEMP - WAX + 1NR ; number of Revalues

58 SLAROM: ii rniln fnr Till Ilnmimrinliii filriilrl f Fill ITMrtiii IAERI1294

(— DO 1000 1 = 1 , MAX# 4 ((SIG1D(M,J,I), M =. 1, LNMAX), 7 « 1, MXR1D)

SIG1D ; 1-Ddata#5 if I.LE.MXDWNE ((STRE(J,M,I), J * 1, MXDNSE), M = 1, LNMAX)

if ISWH.NE.0 (STRE(J .ISWH.I), J - 1, IMAX)STRE ; elastic matrix diU

#6 ifI.LE.MXDWNI ((STRI(J,M,1), J * 1, MXDNSI), M = 1, LNMAX)STRI ; inelastic matrix data

#7 ifI.LE.MXDWN2 «STR2(JM4), J • 1. MXDNS2), M - 1, LNMAX)STR2 ; (». 2»; > matrix data

DO 600 M - l , LNMAXDO 500 MT-l.MXREAC

MR-NR(MT.M)KT -MSF(MT.M)If MR.EQ.C.OR.KT.EQ.O go to 500

#8 if MT.NE.6 («FTABaK,N,I,MT,M), J - 1, MXSIGO), K • 1, KT), N - 1, MR)if MT.EQ.6. AND.LA(2,M).GE.I

<((FTAB(J,K,N,I,MT,M), J - I, MXSIGO), K - 1, KT), N - 1, MR)FTAB ; F-table

1—500 continue1 600 continue—1000 continue

#9 EOF

(2) JFS-2 Library Format (binary)#1 NCODEL(LNMAX*), MSF(LNMAX), CHI(IMX**), FT(3), TAB1{6), TAB2(6),

AW(LNMAX), DU(IMX)NCX>DEL ; nuclide code numberMSF ; oo-values table index ---MSF*0:no F4able,

MSF-! :TAB1,MSF-2:TAB2CHI ; fission spectrumFT ; temperaturesTAB1 ; oo-valuesTAB2 ; oo-valuesAW ; atomic weight in a.m.uDU ; lethargy width

I— DO 100 1 = 1 , IMAX***#2 ((SIG1D(M,L,I), M = 1, LNMAX), L - 1,7),

((STRE(J,M,I), J « 1,30), If - 1, LNMAX),((STRIN(JJ«,I), J > 1,30), M - 1 , LNMAX),(«((FTAB(J,K,M,N,MT,I), J - I, 6), K - 1 , 3 ) , M - 1 , LNMAX), N - 1 , 2 ) , M T - 1 , 5 )

SIG1D ; 1-D data — L: 1/2/3/4/5/6/7: • / * / . , / , „ /STRE ; elastic matrix dataSTRIN ; inelastic matrix data - - - *•-. = «.-» + o.i.FTAB ; F-Uble---MT: 1/2/3/4/5: / / / /« / / , / / i / / . ,

—100 continue# 3 NC1.NC2

*LNMAX ; number of nuclide

J A W ! * . 6. Ffc Requinra«iti

**IMX

***IMAX

LNMAX is 20 in the original JFS-2 library.LNMAX is a variable in the revised system.

; if MAX = 70, IMX = IMAXifIMAX = 25, IMX-30

; number of energy group (70 or 25)

(3) Aakotropk Scattering Crow Section Library Format (binary)#1 NMAT, MAXPL, MAX, LDMAX

NMAT ; number of nudideMAXPL ; the order of Legendre polynomial expansion + 1IMAX ; number of energy groupLDMAX ; maximum sink group number

#2 (NCODE(M),M*1,NMAT)NCODE ; nuclide code number

i—DO 100 I - 1 , IMAXr-DOlOO M-l .NMAT#3 ((STRPL(J,IP,M,I)I J « 1, LDMAX), IP - 1, MAXPL)

STRPL ; anisotropic scattering cross section which is nomalized by »«.— 1 0 0 continue

#4 EOFAt the present stage, users can utilize the following libraries produced at JAERI.

o JAERI Fast set V2

o JENDL-2B/70

o JFS3-J2o JFS3-B4

Type (JFS2 with R parameter), Group (70 and 25) Nuclear data(original + EN!)F/B4">)Type (JFS2 without R parameter), Group (70), Nuclear data(JENDL-1,2)Type (JFS3), Group (70), Nuclear data (JENDL-1,2)Type (JFS3), Group (70), Nuclear data (ENDF/B4)

When users want to produce some group cross sections of nuclides not prepared in theselibraries, or a completely new library based on other nuclear data file, they can use the group

Table 6.3 Nudidet contained in JFS-3-J2 library

No.

123456789

1011121314IS16

Nudide

U-235U-238Pu-239Pu-240Pu-241U-234Th-232Am-241NiCrFeMoCuIfnSiAl

CodeNo.

9259289499409419249029512824264229251413

JAERI-Futlet V2*

ye*yetyetyetyetyetVM

ye*yetyt*yetyetyeiyetye»

No.

17181920212223242526272829303132

Nudide

NaCB-10H-lU-233U-236Pn-242BeB-llOT«-181Np-237Eu-151Eu-153FP(U-235)FP(Pu-239)

CodeNo.

116

1051

923926942

4115

8731937631633995999

JAERI-Fastwt V2*

ye*yetyeiyetyesyeiye*yetyetyetnonononoyetyet

thorn the nuclidet contained in the JAERI-Fut tet V2.

SLAROM: A Code foi Cell Homofeniz»tion Olculation of Firt Reirtor JAER11294

constant production code system TIMS-PGG1'*. The code number of nuclides is shown inTable 6.3. The group structure is shown in Tablt 6.4 for the JFS3-J2 and in Tabla 6.5 for theJAERI Fast set, respectively.

6.3 Auxiliary Files

The auxiliary files required in running SLAROM are shown in Table 6.6. Units 8 and 71

are the cross section library files. The physical contents are briefly shown in the table. The

record sizes of auxiliary files are shown in Fig. 4.3 as a typical example.

Tabte 6.4 Seventy group structure of JFS-3-J2 library

Group

123456789

1C111213141516171819202122232425262728293031323334353637383940414243

Upper eneigy

10.0 (MeV)7.78806.06534.72373.67882.86502.23131.73771.35341.05400.820850.639280.497870387740301970.235180.183160.142640.11109 (MeV)

86.517 (keV)6737952.47540.86831.82824.78819.30515.03411.7099.11887.10175.53084.30743.35462.61262.03471.58461.2341 (keV)

961.12 (eV)748.52582.95454.00353.58275.36 (eV)

Lower ozteify

7.78806.06534.72373.67882.86502.23131.73771.35341.05400.820850.639280.4978703877403019T0.235180.183160.142640.111090.086517

67.^7554.4 '540.86831.82824.78819.30515.03411.7099.11887.10175.53084.30743.35462.61262.03471.58461.23410.96112

748.52582.95454.003S3.S8275.36214.45

(MeV)

>

t

(MeV)(keV)

(keV)(eV)

(eV)

Lethtiiy width

0.2500.2500.2500.2500.2500.2500.2500?.5O0.2500.2500.2500.2500.2500.2500.2500.250.0.2500.2500.2500.2500.2500.2500.2500.2500.2500.2500.2500.2500.2500.2S00.2500.2500.2500.2500.2500.2500.2500.2500.2500.2500.2500.2500.250

JAERI 1294

Group

444546474849505152535455565758596061626364656667686970

6. Fie Rtquinmeats

Table 6.4 (Continued)

Upper energy

214.45 (eV)167.02130.071013078.89361.44247.85137.26729.02322.60317.60313.71010.6778.31536.47605.04353.92793.05902.38241.85541.44501.12540.876420.682560.531580.413990.32242 (eV)

Lower energy

167.02 (eV)130.07101.3078.89361.44247.85137.26729.02322.60317.60313.71010.6778.31536.47605.04353.92793.05902.38241.85541.44501.12540.876420.682560.S31S80.413990.32242

10"J (eV)

Lethargy width

0.2S00.2500.2500.250O.2S00.2S00.2500.2500.2500.2S00.2500.2500.2500.2500.2500.2S00.2S00.2S00.2S00.2500.2500.2500.2500.2500.2500.250

10.650

61

Tabtt 6.5 Seventy and twenty five group structure of JAERI Fast Set V2

70 group

123456789

1011121314IS1617181920

25 group

1

2

3

4

5

6

7

8

Upper energy

10.5 (MeV)8.36.55.14.03.12.51.91.41.10.80.630.500.400.310.250.200.150.12 (MeV)

100 (keV)

Lower energy

8 3 (MeV)6.55.14.03.12.51.91.41.10.80.630.500.400.310.250.200.150.120.10 (MeV)

773 (keV)

Lethargy width

G.23S10.24450.24260.24290.2S490.21510.27440.30540.2412031850.23890.23110.22310.25490.21510.22310.28770.22310.18230.2575

62 TInimir ft rmirfmrniHiwimaimimrv--• -in*nfrmimnui JAEMISM

Tab* 1 5 (Contiaucd)

70 group 25 group Upper energy Lower energy Lethargy width

2122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

2S

77.3 (keV)59.846.536.027^821.516.612.910.07.735.984.653.602.782.151.661.29 (ktV)

1000 («V)77359846536027821516612910077.359.846.536.027.821.516.612.910.07.735.984.653.602.782.151.661.291.000.7730.5980.4650.3600.278 (eV)

59.8 (keV)46.536.027.821.516.612.910.17.73S.984.653.602.782.151.661.291.00 <k»V)

773 («V)59846536027821516612910077359.846.536.027.821.516.612.910.07.735.984.653.602.782.151.661.291.00.7730.5980.46503600.2780.215 (eV)

0.25670.25160.25S90.25850.25700.25870.25220.25460.25750.25670.25160.25590.25850.25700.25870.25220.25460.257S0.25670.2S160.25590.2S8S0.25700.25870.25220.25460.25750.25670.25160.25590.25850.25700.25870.25220.25460.25750.25670.25160.25590.25850.25700.25870.25220.25460.25750.25670.25160.25590.25850.2570

IAERU2M C.

TfabtoM PJJe name aad pkyaical cottMt

UaitNo. Vaxbbbi aabroutaw aim («/W) HqntaH optwt iM i w i h

PDSIN

PDSOOT

1 ISCR

LHOIIOIfCOUTHCIN

LHETEMCOUT

IDANC

PREDIT(V}, PREPDS(W),BSEARCR/K1). EDITS(R)

JAERKR/W), HOMOXS(R)KINFHH(R), PREDITCR)WP3F(R)

JAERI(W),PREDIT(R),EDTTS(R), REACTXR)EINED(W),SPD2(R)

SLA1DF(W), CYLNDF(W),JAERKR)TEDIT(W),1NP2F(X).RBACTgR), BDITSCR)

PDSfcfmtflb

PCS output fib

Hoaaogaaipm Jffaatoa coafficiaat aadB'wadiiDB1 t a n

Effacth* addOKopic croai aactfca of

laput 61* of iaWd flux gum ia PUF•tap

Effactfo adcronopic croaa ttcUoa of

Crow ttetioa for partwbatioa ctlcola-tioa

Daaooff factor

Naatnafawiaotl

s6

7

8

9

10

11

20

21

41

42

43

54

SS

56

71

72

73

•0

90

IFS2JFS3

IAER

LIBR

MACR

X

I NNN

LIBPL

LB

LDEN

UIRD2(R)UIRD3(R),RDJFS3(R)

LIBRD2(W), LIBRD3(W),ESLMJ(R), INPT<R),JAERl(R)

PREDITCW), 1SEAR(R/W),INP2F(R), 1NP3F(R).EDITOR)

PREDIT(W), BSEAR(R/W).PREPA(R), EDITOR)SIGRD(R)

FORM(W), EDITOR)

FORM(W), PREPA(R/W),INP1F(R), INP2F(R).TEDntR). EDITOR)

EDITS(R/W)

INP1F{W),INP3F(W),PAIN(W), PREPACR/W),PAEDTCR/W), ESWJ(R)

PCOUR/W), PU(N(R/W)

ESLMJ(R), INPT(R)JAERKR)

PREDITCW), EDITOR)

1NPT(W),EDIT(R),EDITOR), REACTM(R)

1SEAR(R/W)

EINED(W),SPD2(R)

BSEAR(R/W)

SyatMl yjrMa4 ovtfwt fib

SyMM cart pvach out f i t

Cro« eactioa library for JFS2 tad JFS3

Croaiaactioa

Micronopic croai aactlok for «ach

Total e n d Nction

DanctkNul coUaloa probability

COMMON/LAMPq, bottopie colbtoa

Para taUa for OOIUOB proaaWalty cal-

rahtioa

Midoaeopic croai tactioa (M1CED- 1)

bpat datt ia PATH aad PUF itapt

Scntck fit* for bnckVac aaarck ciScidt-tkw

Ubnry for P, oompoaaat of Kattarn*BMtliX

Macroacopic Pi ooanpoaaat of *acklaajoa

lapntdau

Mkcioioopic ctQM Mctios oocnctsd by•DB* M m to W aa*d ia tacUiacaMrckNonaalaa4a#>Mr«u

Total c a w woUoa ootneaa* fcy V>ft a n to ka «ati ia WcUtaj aaarck

SLAROM: JAEXI12M

7. Sample Input and Output

Two sample problems are presented in the following. The first one is a one dimensionalplate cell consisting of 14 regions, the second is a square cluster of 16 pin rods. The input dataand abbreviated listing of the output are given for these problems.

7.1 One Dimensional Slab Cell

Sample problem 1 is a typical plate cell encountered in an analysis of a fast criticalassembly. The unit cell of core region is modeled by a one dimensional infinite slab cell andthat of blanket region is by homogeneous medium. The cell arrangement is illustrated inFig. 7.1. The critical buckling search is performed for the core cell. The cross sections aresaved on the PDS file with a member name SAMPL1. The microscopic cross sections of 3 H Uand ^ P u are also saved. In RATE step, the in-cell reaction rate distributions are computedfor these nuclides. The 70 group cross sections are collapsed into 8 groups by using the neu-tron flux obtained for a spherical model of the assembly as shown in Fig. 7.2. The sampleinput is shown in Fig. 7.3 and the output list is in Fig. 7.S.

7.2 Square Cluster of Pin Rods

Sample problem 2 is 4 X 4 square cluster calculation for pin rods. Geometry is illustratedin Fig. 7.4. Since this model is octant symmetric, only one eighth of the unit cell is explicitlydefined in the input data. In PREP step, a single pin rod model which is consisted of fuel,cladding, one sixteenth of sodium and that of mini-calandria tube is used to prepare the regiondependent effective cross sections. These four materials are assigned to the correspondingregions. The computation time significantly depends on the parameters IBOUND, NGR andNDA. Table 7.1 shows an example of computation time, cell eigenvalue and one group cross

NO

Thickness (cm)

sus iiiiiiiiiiiiiiiiiiiiinTTm; o. 2200EU i ^ ^ C ^ y S S ^ ^ 0.3175No 0.6350Pu ^ W / W / Z W / 1 ^ 0 .1588A ^ 0 s JV-;-:^:::-^-^.-'^."^ 0 .3175No 0.6350Pu '(/////yyx//s/////7Z 0.1588

0U02 0.6350Pu W///JSS///SSWM,. 0.1588

No 0.6350

AJ,OJ H^^:v-:-::;'-a-"- 0.3175Pu V»S»?MJ/WM//,. 0.1588

0.6350

rlem) 0. 31.49 61.49

Fif. 7.1 Cell arrangement of Maple problem 1. Fig.7.2 Spherical Model of critical i nMy.

JAEM12J4

sections for this problem. Though the boundary condition IBOUND should be 1 (periodic orreflective) striktly speaking, the isotropic (white) boundary condition will be realistic in aview point of a computation time and a reasonable accuracy can be expected in this case.The input data are listed in Fif. 7.5 and the output list is in Fig. 7.7.

«« SANPLl • •

PREPSAMPLE PROa. 1 CORE CELL • • BUCKLING SEARCH • •

*2B t4 t /300.0 1.2S 0.0 /

0.2200 0.3175 0.4350 0.1SM 0.o.isaa 0.4350 0.3175 o.isaa 0.24 1.4043E-02 24 5.113*1-02

t2S (.52001-03 *2B 3.311*1-0211 1.443*1-02 24 4.04301-03

t4t 1.B147E-02 t*0 1.S4ME-0324 4.15301-03 24 1.M20I-02B 5.4t42t-02 13 3.77101-02

21 3.24001-04 /11 1.443*1-02 24 4.0«3*E-03

»*» 1.11471-02 t« * 1.54*N-*324 *.IS!*[-03 14 l .MlM-ai

*25 *.000*1-03 t i l l . t t ** t - * l«4* 1.11471-01 *4* l.S4Mt-*324 4.aSS0I-03 I t l.M2*E-0I11 1.443*1-01 24 *.0*3*1-03* 5.4*421-01 13 3.77101-01

1* 5.24001-04 /*4t l.ai47t-01 **0 1.14301-03

24 4.B5S01-03 24 1.1*201-0211 1.443*1-02 24 4.04301-03

*25 1.52001-03 t i l 3.31141-021 3.14741-02 13 3.*114t-02

21 5.24001-04 /24 1.40431-02 24 5.113*1-02

PATH

21 4/. 2 4 1M l 1IS 224 1

2* 1»41 1aa 2a 3

• 4 1 12* 2.24 1.24 1,

t * l 1,ia 2,24 1.

/24 1.

2B 4.

3175 0.4350 04350 O.ISSa 0..1220E-03 /

.4*221-02 2* 1.

.S2ME-04 13 2.

.31501-03 /

.20201-03 24 4,

.4*221-02 21 t .

.520*2-04 13 I .

.313*1-13 /• t *MI - *2 /.120*1-04 13 2..315*1-03 1.4*121-01 2* 1.•lOltl-W I t 4.

.51001-0* 13 2.

.31501-03 /

.4*221-02 21 1.

,20201-03 24 4.

,12201-03

SAMPLE PR01. 1 CORE CELL • 14 REl lONl •70 14 2 1 2 0 0 /

0 0 1*0 0 /

0.0 0.2200 0.5375 1.1725 1 .3.0774 3.2344 3.1714 * . l B l t 4.5.5203 /

PIJF

2(0) 4<0.0> /0

EDIT2 2 0 0 /

C0REC1RATE

REACTION RATE I N CORE CELLC0REC1 SLAROH

PREP

1 13 14 15 143313 1.441* 23*77 4.tB27 5

SAMPLE PROS. 1 BLANKET CELL • • HONDtENEOUS HOtEL •>

300.0 0.0 0.0 /521.OUt

»2S *.4M0E-a5 *21 4.0175E-0224 1.B27E-03 /

BLANKTEIND

SAMPLE PRO*. 1 • • SPHERE • •1 2 54 2 70 30 B 0 0 - 1 0 /1 - 1 1 - 1 - 1 0 1 1 /40 54 /5 10 IS 20 25 30 35 70

l.OE-05 l.OE-0* 1.0 1.0 0.5 10.71725 2.1*3 1

C0REC1C0REC1•LANKT0 . 0

SAMPLE

.ISM 0.435*

.ISM 0.220* /

.1*041-03 /

.4*701-03

,37Mt-*3

,M*M-*3 /,4*7*f-(I

4*7*t-*J

MOOI-03 /37*01-03

40701-05 •

11001-01 /

3711-03

/

.213B 2.4424

.1415 5.3003

0 0 1*0 /

24 4.4S21E-S3 2* 7.*4ME »4

COLLAPSIN* INTO 27 (RDUPS

1

100200

3004MS M

•007MM O* M

1 0 Mt l MM MtSM1 4 MI S M1 4 M170*M M1*M2 M *21MM M13M* 4 M»SM24M27M2M02*003000310032003 3 M3 4 M34103500340037MJSOO3 * M4 0 M41M42M430044004 5 M4 7 M4 0 M4 * MS M *S I MS 2 MS 3 M5400*5M5 4 M3 7 M5 * MS M *M M4 1 M4 2 M4JOO4 ( M4300440047004*004*00700071007200730074007500

SMPL1SMPL1

SANPLlSAMPU

1AMPL1SMtPLlSttDPLlSMIPLt(MPL1SADPL1SADPL1SAMPL1SIMIPHSADPL1

aaaniBADPLlaaMPLtMM*11aMm.1SAMPLltAttPLiSAHPL1tMtPLlIMHtSAMPLlSAHPt.1SAMPL11AMPL1SMtPLlSMH>L1SMtPLlSMtPLlSMtPLlSANPL1SAItPLlSANPL1SAMPL1SAMPL1SANPL1

t**PLlSAMPL1SANPL1SMIPL1SAMPL1SAHPL1SAItPLlSAMPL1SAMPLlSAMPL1SMPL1SMIPL1MHM.1tMtPLlSAHPL1SMIPL1SAHPL1SMWL1SAHPL1SMIPL1SAHPL1SMIPL1SMIPL1SAMPL1SANPL1SAItPLlSAMPL1SAMPL1SANPL1SANPL1JAMPL11AHPL1SAHPL1

Fit. 7 J Input data for sample problem 1.

SLAKOM: A C * * * j r O * l OdodMiai of KM* RMOtoc MOtlllM

IGT«9

RPP12)

RPP(U

NX '3NAPIN * 2NDPIN * 2IDIVP * 0

NZ *12NR * 8IBETM-45

RX(I!RX(2)•0.

RXU) RX14)

Flf.7.4 O*U i i r i i iwMt of w p U problMP 2.

TaWt7.1 CoMpuiwaof ooapuutiomtiincuidpkyfictpanmten for 4X4 tquut chutar

IBOUNDNGRNDACPU^dec)*-

<s.>

CMtl

11020

4681.36556.292-3b)

4.614-3

Gtf§2

18

10193

1.36406.254-34.592-3

CMO3

0102094

1.36446.284-34.612-3

•) Computation time by FACOM/M380b) Read M6.292X10'3 bam/cm1

. . SMWL2 • •

PREPSAMPLE P«0*. 2 • 4 *E«10«

3 0 0 . 1 .30 0 .• S I S

0.413 0.0*01 0.17*31 0

PIN CELL • *l««0.0 949 0 /

.073U»51 t.4*4*E-S *42 1.7044E-5 *41 *.*O4*E-S

*4* 2.»13*E-3 t i l l.**l*S-l24 4.4404E-2 14 1.3132E-224 7.4415E-411 2.3374E-224 3.S1UE-2 24 4.4011E-324 2.40tlE-4

PATH* » 4 1«UME CLUSTEK Or PIN

7 0 4 2 1 0 0 0 /

3<7> 3(*> 1 2 3 4 5 4 /

0. 0.24172 1.52272 2.71272 .O.*2772 2.11772 /0. 0.423 0.5131 /

PUP37 0 5 3 0 1 0 * /

2(0) 4C0.)0

EtIT2 2 0 0

f«HPL2

*15 1.3I53E-4IS *.M43E-4

25 4.M0IE-4

4 A 9 A 9 A A V AXV CM C M 4 3 V

1

*40 4.5U3E-4• 4.S743E-2/

2* 4.4535E-3//

2* 2.1S11E-3/

1M2M40*5M« • *7 M•00to*1000

1200130014001500140*170*1*0*190020*02 IOC220023*024M25*02M*27M2*0*2*M3M031M

SMtPLlSARPltMOPL1SMPL2SMPL2»«KPL1tMPlt>M*PL2tMm.2SMIPL2

turn.!SANPLlSMIPL2SMPL2J4HPL2SMWt.2«MtPL2JMtPClS M W . 2S M W . 2tMW.1tMm.2IMIPL2SDMPL2t M P l ltMm.2tmnxIMWLlSMIPL29tkNPLt

Iatwtdatafors«npkproblm2.

IAXRI12M 7.

uttwant MM. 1 can cau. • • MUIIM MMKD •>

WMMt •* *MIM*«7»n«CTRic*i/*MiMi•/t«,i/tti H nn•/•MI«•M.I«M•'•UI.I/CVUIMICM. UN« I • ' T I M » 1 I >

LMUI IN. tP MMIIM ZN JMH . tf KltlMt XT I-MCTMMMM M. IP 'HUM IHtUM

•tMIIM. FMMT LIMMT > **T1M l i l t

•IMKI.IM. U PIIUM (MCIM Mf — >m » » IM. *f MKTIM M %•* MT» — — • • • • • >•tHUIllMLMTU MTIICn M W I I U W •••••• IMMMtiMi. MM MM* t» tunic w i n — *MtMIMM. i n MM* *P 1M1MTH Wllill — MmtMIIHU. IIW MM* •» Ml MTMM TtMKHILMIt HMir MM* M. •» KMTIC — H•mMiiiMiir H w i M M * M . •* tMwrric — u•MMIIMIT IHHI MM* M. *P «M • _ — rMMMIM. *f MKT1M W >-TMLt —» «MI1MIM. M SIMM — t»n <M. W TWHMTMI • — — — _ • — — »KM IM. M H-HMMm — — —i n n IPHIIIM w KIMMM HT« •

IMN.I MM. I <tM CHI • U MtlMM •• • • (Tl* • • • I*MT *M HJ • • •

M M t m t»M > C IIPMIII ILM• M « K M - UMltM ItMMMI W T - MtltM ItM H I W I - MtlMt MHMII t» > - MtltM MMitt m u m cMtiriM <•!,*,i,i>•IIICTIMM. HI <t,»l• M l t» I M • MMMMMI W TMTA M T MMTITM. IMMtl «f *M MM• M l IP HIM! M Ml Ml «M»H K IF LtTTICt CH.U TMCMMint CMTML If *IJ «.1>• M l W MMt MtlM. MTHMIIMM. *P I1V1SIM fM MMLM IITHMTIM• M l IF MHMLM m i U M III t Pl« MlIMltlM IT t** M.l . t )•MLt IIHI IT MtHI IMPLITtl I*TIM ll»l> •

Ml ID.1 « 1 < ) « 7 I

11 11 1> U 1> It

«BMTIIIM. M. i l ••>i i t t t t r *

11 11 U U » It

•n«>l UVXtlM n *••> i.iiiiiiin «.wmiM M i m w M B I W I I (.UUMMI I.IMMIHI I J H H M I *.MrMt<M MHIIIIMt.MTUI»tl t.UMtt**! ••4S4m<«l ft.4Min«« «.SUIM«M I.NHK*« tSSMM**!

n u n ••» u » P*M MMt

•TMM Wtt U » PMJI MMt

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1 LM1ML MCMM H TM I l i l IMW MITTM M TM} HLt MIT " 1 • • •

LIT MTMMTM TO MM.TTICH1.WMH iti.titiii U I . H H H m . m t t t i x . m m

ID1.IIIIII 11)1. 1U1.NHH ll l l . t l l l l l U11.MMM

init .HMtWI If T-MtllM MMUCMLTIIItMtTM TO MM.TTICISwiNlfn 2tVkW9VvV m « V V V N v iiHtWVVOT 9*X<tll.MMM W1.IIHM 11H.HNH tllt.MMM 1S)1.MMM

I LIMt MMM • • • WLt/nm TSM « MC

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•LAMM: ACMtfcrCUHti I of MM MWUM

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(KT.KMI MW.MMf IM,nTM..«MM»inn au HM MM M,U<UM,MST»>ITI i IUI MM «.»tuw,mn»MMT CMTMl ( • , l ) [Kir .m»>•-SICT .MUM .HI , n « M.MWKI

1M

ITIMTIM PMMCTBMM l .tv I M U 1TIMTIMI PM MTMMU tP MTU 1TMHIMI• n u n MTMMUTXM• M H • ' ITUITIHH TMTIIniaiwH nutTKMITM MiaTM.I>IMIP.M»TICMVMMKI caiTMIM •# IMM I.1MW-IICUHMKI CaiTMIM «* HTM t .•anMMUTIM UITMIM•WI-MUUMTIM CiaiTlM.)MI latMMUTIM • .MM PMTM « »»M IIUUIIII

••MMDIM. CM! M W n

•TMM UNI IMI PM* MM* MIM MM 1IMM

rlJMi»i»i« IMTU MM. I tMI CCU • I t MIIMM •ITIMTIM I N

MTIII iltMTIM CMUr IWLttHICniM MtTM t.lMMIMIMUTIW IMM W tlM« «M.M •.MMM-M•IUTIH MM* M M U •••niMTIM I.MIIM-M

INIMY MOW 1> • MUM. PLM MKI.HI

KwaiT «M«P a

ucaai tawp 3

i.44tm-iai.U4rn-si1.H4III-M

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l.UISM-Kl.TMIII-tll.«IMH-ll

i.mm-u i.titm-u I.«IMM-M I.IWH-Ht.MMH-M I.MITM-M t.UMM-M t.ltfHI-MI.IMK-H I.44MH-M 1.4OTM-U4.4TUU-U 4.4f7t»-*Z i.M44tt-M 4.SM4M-M 4.SI4.4MIH-M 4.HTIM-*! 4.a47MI-M 4.SXM4I-M 4.MPIM-M4.4IUII-M 4.MMK-M 4.II74W-M».T»>n-U I .RHIMI I J H W 4 I t.MtMI-M >.M»tI-Ml.H4>M-ai l .H»H-ai f.MMM-M t.UMN-M l.HtMt-ll9.S7Mtl-M 9.1MIK-M f.l*MII-M

i.uim-at t.nr>M-«I.MMM-M «.44I4M-Ml.MSTM-M t.H4in-*tI.M«tM-M I.MMM-H1.MWM1 I.144MI-M1.4411M-M ».«tan-at

>.M94M-«t>*4W44t-*lI.MUM-*!>*MMM-M

s.mut-M j.majMi

I . H M M I 4.1WMI-M 4.MMII-M t . W I I H I

4.UHM-M4.OUM-MI.tMlU-*!S.M4MI-Mt.UIMt-Ma.nMPI-M I. i.imia-M a.jMMt-w

r.Minc-ti r.MM4t-*iT.MMM-M T.U4UI-*!•.iiun-*t i.*ttTM-«i*.4MMI-« I.IIIIII «1MIIHMI I.4MIM-*I

T.MMH-MT.M4tW-«l

rMMn«i

T.M41M-41».•

a.MMM-*i • . 4 i t n t - «• . 4 t n U - « I.4IUH41I.WtlMI

i.aMtM-ai «.4niM-*i <.itMn-*i <.HHti-n

Fif.7J (ooatWMd)

JAEM12M c. n*

• • • • MTNT I f TItIT • • •

$um "moo. 1 com CEIL > M MUMI >

• I I H W I OP > » I M > - 1 .MM (IHMtER OP MATERIAL S'IX»> «1«» CHVfltZft OF INEHT KR«1M > «7«lRWZ CFLUX 1«C Z>WIT4 » • ZIRP fMJ 0*M 1*C t-WIITXt) • 2IIRECTOIRECTIORAL H M .

1 » H Z>REAt > • ZRACT4MMOER OF ACTIVATION X-SECT- 01RKECCX-SECT1ON

• • M 1"C ZalKITlt) • zOtITFUT OF HONOIENI2EI X-SECTION

« E l P t 3

CELL >V1<UE RMIO«C«-ALL,1«PARTIAL,Z-TAREM> •

IIHEHIIOR UBEi 1104* FROM 3 M MREITRICTIt RIIIWI A » M T 1 I U L - I I U H M l * 1 EJOZ" 1* t i n * 1 M l * 1*

CKPFICIIHT CtMTtWSO

713I t

3137434 tS34 1C7

1 T I

13It

31S7434 tJJ41

17

13I t233137434933t l47

4.23432*414.131(1*41•.10971*41•.USSimt.rooti***4.44(41*44• .71771*4*4.41111*44MIIIIIHt.THlKM4.41111*44

•14M14313 *44M34

4 1

«.2ISTB**II.1H4M10.1I32I**!

4.13401*44l . tHNiM4.74*41*044.43171*44* .7»M*444.7IMf*44t.S94M*l«

•HW ilFPHIM CHPPICIMT t lM IU II.IS4ll*4t

0?107 l l * l l0.11321*41Q.7033B*44

o!?l?7|.K>

Q.7421E*40Q.42I9E*00

0.1S19E*010.3OS0E*010.23492*010.1339E4010.11071*010.13*41*01

0.74772*000.4393fi*000.43112*00O.H30E*000.50711*00

It101431sa4430

424B

2a14

20Z t

304430344240

4 .1MM*t l4.11111*41

*!l394I*444.419*1*44

4)41411*440.71471*444.74971*4*0.31171*04

0.19731*010.22431*010.1S3*E**l0.1Z41B*410.9734t*M

4.72M1***4.44031*044.74912*444.77141*44

3•

I f1 1I T33I tI II II T4149

1

11II17

394111374349

39

13

17

39433 13743

4.W4M*41

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4.49471*404.349*1*44.4.72471*44**M3M*00

4.24111*41

4^11411*41

4.11111*44

• !r4IH*00e.443H*44

4.23711*00

4.1474KI14.1M3C«4I*.133H*01

4.93IH*94

4.44392*040.74771*444.71431*044.344K*040.73321*444.34712*44

4141 12220344444»344470

41414II

34toi tI II I4 t74

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4..749II4O9

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4.14171*41

4!ltt*t*414.91111*444.32474*44I.744M*M

o!'TI4!l*444.730*1*44O.S11H*440.21441*00

0.243(1*410.1*341*410.12B4K»41

•.47441*44«.7St4E*444.7417E*44*.S704E«444.38S4E*40

I11172 129334 14713194 1

111

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31117232 t334147333913

4.13411*414.174H*414.1114**41

4.I37M***

4.44141*44O.l l tSI***

1.1(941*411.17141*41

1.11711*444.1K1K44

l.ail4l*044.440H**40.3(441*44

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e.OI44C*444.42Z»*44

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121 *243 *34134 *344 44 4

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4.313M*44

4.1349**410.7IMUMI.4WMI*.MMt*M4.7IIMX4I.4MH***4.3HM*44

0.440U***

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4.49394*44S.*UU*M

•.Tn*a*M•.»!MoM

tANE OF TM1S M**LEH> C44.ECI

MKHR COOICltO 4F l I M n 111 II SIMM IR 9*1 FILE

K M CMIC10I 4f LE44I» 2*7* II 1T4M4 » 9M FILE

MMKR CMICIM * LEMt» 7* IB 1T0M4 u 9 H F1LI

HICM t NCHMR RAM * f THia IHVtOLaiHIHIH* • t M M l

M M f l CHIClt l 4f IIMTR 2*7* I I BT0H4 » 944 FILE

H i m CWIC112 4F LIHTR 1474 I I 170444 u f M FILE

(continued)

TO SLAROM: ACafeferOril CktaMioa ofFM ftnctor JAHU11M

I MTE •>»•

RESERMI KM«r >19Mt I HE! MNMr • 432*

T l.lHIIHt • • .MSMMI t t.UMKH13 O.4SSM«*O u i. inmn is i.isuitto

nT m now CMTRXWTIORS MI w m i m .

SRQU* REACTION *E«IOR -

• • • TOTAL REACT2M tATE

RU-F1ESMF1SSM

AMMPTIMW-P1SSM

P1I IM

AIMWT1M

PISMN

MMWriMMI-PIMM

PISSM—WEI AVIRAII PIII.PJICM.

WKl» - «4»

HHP P.IACTIM t t l l M -

• • • TOTAL REACTIM RATE

AIIMPTIORRU-P1SBM

AMOWTSM

P1SSON

AUORPUMRU-FISIOR

PISSOR

AIIMPTIMNU-F1SSM

FISSOtt—USEt AVERASI PLVR,MCDft.

••a PDEP aaaa

U N I LIST

14u

14

(PM M«W) " a

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t*MMII-*l

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12

I.IU1II4M2.44S32EM*

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t'.rmut*l.MTtM«M

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3.HMIEIIS

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I.U113EO1a.MMIE*«li.mtiMi2.1>3«21«ll4.1414M*!!

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nMT«lC.»t>lWlCO/TI,lfT*r PM MTO.P1JPOfMM.ldWTEMSfSLU.lfOLItWIICM. M*•OUT OftlMO.t.t. . . .)•FTIH 1 MTFtir HICH• r rm . n. CMPWMT WMIwriw • MCILIM i n nLWUR IM. •* RML1H » JPtM. V M«Xtm P«T R-IMT1IMCKf M. (P PIIIIM 1PHIRWM . *p m m iRt»pt nUSE* «R«F" CWtriMirS — ITtt • I

> • — JFI-J l »• JPS-t P1MH Lit

-1 JFS-I M >-HUU< -1 JPt WltHU. Lll

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VPFSvtv HHW ^ fNRMKLtHt. OF F1UIM 1MCTHA « T — « « « — - )RKK» I N . OP It I ACT I M IN l-» ftATA — - — — — «dXMIHMX. SINK M W f Of CLUTIC MTII I I — — MNKMtltMX. SINK VUVtP OF 1HLMT1C MTKIK — MMIIN»tMX. SINK <RW» OF KM N t l l l — — MNKRUCtNO. BF ItUCT^M IN *-TMLt — — — - — 4NXIIHtNO. OF t l tAM — •MYlt fsVA tlft Y T I I A B I tvviwa ^

• M 1 M SEPEWIRT TtftmtftTMfs*a.w

MIMIR IP sinmr

(co»tl— id)

MERI12M 71

- ""—'«• i w u i a TITLEi • • inm • • CKutnin « ir men

I M PUT C>»

• 1

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NEIION NO.

H W NO.

HIM ICHTTMIM

w u m i m w ao.

uu.cw.moa onioao • run1 - FLU UO MMOTt - Mjomr

nmiw> U N no.» U N » MCM HO.

F I I I I M onciiHM M M0 - MM M l> - MM CMM

•NWT MTA LISTo.iMiiwixrO.tMIMllltOOO.ttMOIllKOOO.IOIOIMMtOlotoirwiHoi

O.lTfTOOOH^S

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O.10»7O7M-M 0.1017»»Mi-MO.I01MHOI 01 o.loMlMtl-OA0.M7MI0M-0S O.fUl»m-»0.07II0010E.0S O.0I7IHUI-OSO.nMMUI-OS O.7STOW71I-OS0.4»0M»E-0S (.HKIIIII4!O.«7t»lME-II O.t»TUtll-OI

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1NTI0MTEI OOWCE

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• ••^•hvabAO^F^fiaBBA A •••|aai*BHl«#J» A^rV • VTv̂ ^BrK v.^V .J . W # o>̂ V 1WWV

— l.oirumtoo

C«tt MtOMCO r iU IM mCTIMM

U1IM0K-0I

l.UlM0t-0t

».MSMSI*M0 . 00 . 00 . 00 . 00 . 0o.o i

I.14IIS4N-ML.ttMTM-tt

i.oumt-ot1.711UM-0Sl.«0t>*M-0ft1.1SM0M-0II.StlHM-MKO1.0ft.O1.01.0. 0

MWEK tpWLI I I OP LKMTN

WM0U SMWV1M OF LCttlTH

nmout SMmtSf or LKMTM

K M I I SMMiti Or LKMTN

nmoKO smMiit or LKMTH

MHOIR I M H l t l Or LKMTH

WHOM SMWfXSO OP LfMTH

ntnoH simniiff OP LKMTH *

MKOKH HWflltl OP LKMTH

I .40M1H-MI.OMAOOt-OII.741HM-Mr.»tmc-oiL.S09UH-01

i.o1.01.01.01.0

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o i i irotKO

1S2 I I ITMKO

niS4MMHttt.4tM11l-Ut.TUOMt-Ms.onoon-osO.ltXUOC-M1,l»lMt-HLNMiH-M0 . 00 . 00 . 00 . 00 . 00 . 00 . 0

in **t riLt

IN M l PILK

» m Pitt

IN » l PXLK

151 XI ITMKO IN m PXLt

IS* I I WHO

«• » turn

0 XI tTOtKO

1 « XI STOMO

IN m PILI

IN m fXLI

IN I>M f i l l

IN m *iti

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lltOTMU-O]).H»m-«:

l.MOUU-0!0 . 00 . 00 . 00 . 00 . 00 . 0o.t

tMll MKM.ED EOOEO

SLAKOM: A C o * lor CU Ho lofhrtltMctor IAERI13M

OMttI POM. I • 4 H U M Fl« Clll • Mart.

tmaamic.xtniMict/TR,l/TOT #M M T t ltrHMal/ac1/SLUft/CVLiaMXCH. KMFMBT OFTIMO.1.1....)

• MTPHf HICM(MaMa>*r tt n w a m oawat aWKLIM OIMCH:•§. OF WCLIM la JFI

no. OF iMioai mi I-IICTUMCMI M. OF F1IUM tMCTMaM. OF IMMr HUFI

Ulll MOW CDMIUII tTK • 1> a JFS-X LIR

a JFS-I FIUL Lit-l - — jFi-t at a-MMca

< -1 JFI M1MM. LitLiaaMT « m i mrttMTiM H I T

IM> >M. OF I H H I oaaa* — — — . — — — ttnoaauiM. OF F I I I I M mcTM HT . . . . . . . . . . . . »man int. tf M M T I M la i-t MT« . . . . . . . _ . . a

HUM* nait oaoat OF UMTIC MTaiM . » . . >atlMW. I I K OBOtt OF laOLMTIC MTaiRIIMH. H M OOMf tF UN WHIM . . . . . .

_ :i»t. » aiKTiM » F-TMII — — . . .miiMiM. OF tiaaM — — . . . . . . .an I M . tt TianaiiTWHi — — - -ma int. OF a~t«UMTia — . . . . . .

am oaaat coaiiMTi it jrt-» na

Klin la iitMwrI • 4 III III 4 • I I I I

14 I I I I » H «l *H Ml 014t » »«• • « t4l Ml Ht t i l

uatiMtmiCMIT.FM alllMMIIV I.F.MULIM

• H I M « H » I « T TianmiTwii3M.M SM.M Mt.M

NUMIIt OF ILIMNtI J 1

HUH WITHO.UMM t.tttlM t.lTIUl

auCLitE tialxTt

s

0.07MM

titMl141Mlt4ttn

4.M40W-*!1.T044M-0I4.tM7M-tSIIWIMt

1.014.WM4I4.IOOm-M

l t lM I.4040M.04

t4tt»M

Ftf. 7.7 Output of aunpk probktn 2.

JAERI1294

1.433U4«-U5.J13MME-0*Z.10977ME-SSZ.0139AS1E-S4B.»3471SE-B45.I112SME-0S4.2HMME-031.3f7*WSE-BZ1.S44W44E-04

11 25 I!If1*3351-0412 2* 1.3243444E-0313 11 «.S72tQff4E-03

NENORr REQUIRED 2 * 1 * WORDS ON PREP (KINFHH)

MCKSftV RftVIftEB *414 WMDS ON MEP (HOHONB)

AT CVLMFTITAl VOLHM t f FUEL R IS I IN1 S.*t1T*TAL VM.WH *F PMTERIAL REIIMf — 1.171

H M H E M M I D1PFWSI0N COEFFICIENTS

s.mmtM 5.tuMi**o -t.M*17S+Ml.9HfBM

f .U3IIE-01,31«3Sf*M.44f*SE«00.4*7»E*W

l.tUMI+H*.St!2SE-017410171flt

1 .tH7f 1 M1.71lf4C+»01 .»74I2I-011300fZI+tO

»HH<H

I . U W K Hl.*77in«M

1.1IWIKMl.SI*t!l«Hi.miii>ii

1.3SI7JK0O1.9n»E<Ui.It7ltl-01l.tflSlt-Bl

3.»itlI>M

lilltUltH

f.TMX7I»M

1.1I17IOHl.»7Mf»M I.IIWKH

l.«MHi«Mi.nr7ti-«i

ioum

PU INVT

10 30

4*4 StUARE CLUSTER OF PIN

•EOHETRY TYPENUN*ER OF I U I - RESIONINUFJIER OF T - REIIONSNUBtEft OF R - RESIGNSNUFWEk OF X - M S I 0*1OUTER MUNtARY CONDITION < - l , 0 , l r 2 )DIRECTIONAL PIJ ( 1 , 2 )NUNkER OF t ON * FtESHNUHDER OF THETA OR T KESHTOTAL NUMBER OF PIN ROBSNUNBER OF R1NSS 0 ' PIN ROB ARRAYNUMBER OF LATT1CI CELLS TRACEDPRINT CONTROL OF PU ( 0 , l >ORDER OF BAUSS RADIAL I~TECRATIDNNO. OF DIVISION FOR ANSWER 1NTES«ATIORNIHWEft OF ANNULAR DIVISION IN A PIN R0»DIVISION BV *PP C0 , l *2 )A M U RAME VI DESREEPLOTCR OPTION (0 ,11

T - I H NO

< OCTANT tvmermc PILLAK VITK tewum AMAV *r nn MODS >

MR NO.4

•••KATERIAL NO./R — •

0.4*1711*00 O.15217E+O1 0.27127E«01

0.0 O.423OOE*00 O.S1310t+*Q

•••FIN tWR-DlVI«ION"«0.0 O.iI3ME*9t O.SlllOt+tO

STRME HIE* 514* FRM M M * » CLVP77-STEP

Fif.7.7

74 SLAROM: ACOo»foiCrtHorootfJurtk»CUc»ktlonof rut Re«ctor JAEPJ1294

i S-K«IM WWtER «•««

aa a a . a

taa 1 a aa 1

•a

aaaaaa

aa

2 a 3 aa a

• aC 7) • ( « aC S> a ( 10) a

a a

a a

C 10) a ( 12) a5 a * a

4*4 ftVAftf tLUSTf* 0 ' PJ" ••a* HATfRIAL JHMWJt • • «

aaa 1 a aa 4

aa

aaaa•a

a 2 a aa 4aa

aa

ama 3 a aa 4

t a a• 4 a 4 a

> f 1) • C 1) •< I) a C I) •

3 a 3 a

a a

( 2) • C I> •3 a 3 a

1) 1.00013 21 O.fWSS 3) l.OOOH 4) O. t fMl S) O.VttM *) 1.00011 7) 1.00004 •> O.ttMS

• ••1422 LINES DRAWN FOR MTM TAILE aaa taaaELAPUB TIME 1 SEC

ITRA8C USED 203t FROM 30000 IN • IJ2-STE*

Fig. 7.7 (continued)

JAER11294 75

8. Comparison with Monte Carlo Calculation

Validation tests of SLAROM were performed by comparing with the results of theMonte Carlo calculations. As a Monte Carlo code, VIM17' was adopted because it used a veryaccurate continuous energy cross section library.

Since the cross section library of VIM is generated from ENDF/B4 in Argonne NationalLaboratory, the present SLAROM calculations use the JFS3-B4 set which has been producedfrom ENDF/B4. It should be noted that both the SLAROM calculation procedure and thegroup cross section production method are tested in the present comparison. We show theresults of two comparison calculations in the following. The first problem is the ZPR voidedpin calandria cell and the second one is a plate cell in the fast critical assembly.

8.1 Voided Pin Calandria Problem

The voided pin calandria was used in the pin zone measurements of the ZPR gas-cooledfast reactor assembly. The unit cell consisted of a 5 .08 - X 5 .08 - X 30 .48 - cm voidedcalandria loaded with a 4 X 4 array of 0 .957-cm (diam)X 15.24-cm mixed-oxide rods.The present model is the same as that used in the validation calculation for the SDX cell homo-genization code for pin geometryu). The detail of the specification is presented in Ref. 18.The SLAROM result was obtained with use of a single pin model corresponding to the SDXmodel. The VIM result is given for a three dimensional model in the reference. Tabla 8.1compares the calculated cell eigenvalues where the SDX result is also shown. The value ofk~ by SLAROM is very close to that by SDX and agrees with the VIM result within a one-sigma uncertainty. The heterogeneity effect J**,, agrees very well between the SLAROM andSDX results, which are comparable to the VIM result.

Tabto8.1 Compiroon of leiults among the SLAROM, SDX andVIM calculationi for the pin cell

Eigenvalue *" Ratio to VIM J*»> (%)

SLAROM 1.2997 0.9984 ± 0.0024 O.S20SDX»> 1.2994 0.9982 ±0.0024 0.S42VIM*> 1.3018 ±0.0032 0.442*0343

t) Mcknight R.D.: Nud. Sci. Eng., 75,111 (1980)

8.2 Infinite Plata Call Problem

The infinite plate cell problem are always encountered in an analysis of fast criticalassemblies. For a typical cell structure, the validation test is carried out. The SLAROM andVIM calculations were performed for the same model where a leakage was not taken intoaccount. Table 8.2 compares the results of eigenvalue and the one group averaged cross sec-tions obtained by both of the codes. These values agree quite well with each other. In Table8.3 the total reaction rates of main nuclides are compared in the absolute values. The impor-tant reaction rates of heavy nuclides agree within one percent between the SLAROM and VIMresults. For the nuclides of which atomic densities are very low, the agreement become, worse

76 SLAROM: A Cud* fat OH Horofiritinn QkuUtion of Fsit R—ctot IAEM12M

due to larger variances. The capture reactions of moderator and structural materials agreewithin a few percent. The neutron spectra obtained by SLAROM and VIM are compared inFig. 8.1. They agree well above 1 keV except for the energy group including the 28 keVresonance of iron. However, SLAROM gives a harder spectrum than VIM below 1 keV. Thiscauses from the removal cross sections of the JFS 3 type set. The fine structure flux distribu-tion in the cell should be accurately calculated in a cell homogenization code. For example,Fig. 8.2 compares the integrated flux distributions between SLAROM and VIM. This cellincludes Pu metal fuel plates, so the flux varies rapidly over the cell. However, the agreementbetween the result by SLAROM and that by VIM is satisfactory.

TaWt 8.2 Comparison of eigenvalue and one croup ctoM sectionbetween the SLAROM and VIM calculations for theplate cell

SLAROM VIM SLAROM/VIM

*-<*E/><2.>

•T

1.71491.009-2^S.86-3170.91

1.713 ±0.0021(1.009 ± 0.00091)-2(5.91 ± 0.006S)-3170.3 ±0.15

1.001 ±0.00120.998 ±0.00090.99S ±0.0111.003 ±0.0009.

a) Read at 1.009X 10"1 ± 0.00091 X 10~*

TabteS.3 Companion of total reaction rate* for isotopes between the SLAROMand VIM calculations for the plate cell

Isotope

"»PuM0PuMIPu235YT

33t|j

NaCrFeNi

VIM <

Production

1.537 ±0.070.0463 ±0.250.0224 ±0.090.00878 ± 0.080.1004 ±0.63

lff%)

Absorption

0.6505 ±0.080.0331 ±0.20O.C0886±0.10O.O04S9±0.O90.2552 ±0.190.00276 ±0.750.00864 ±0.60.0275 ± 0.60.00707 ±0.3

SLAROM/VIM

Production

0.9961.0040.9800.9831.014

Absorption

0.9930.9940.9790.9820.9961.0361.0131.0361.010

8. Comptriion with Monte CutoCilciiktioa

— VIM—SLflROM

10'10* 10* 10*

ENERGY (EV)

Flf. 8.1 Comparifon of neutron tpectnun between SLAROM and VIM in plate cell.

1.80

1.60

1.40

1.20

1.00

0.80

0.60

0.40

( «10>

:

;

• = *

)

tow

«K-;

s

—•—euwwi« VIII

) •

1

j

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00DISHNCE (CM)

Fig. S.2 Compaiiton of integrated flux diitiibution in the plate cell.

78 SLAROM: A Cod» for CtU Ho»ujtdritln« OricuhttoB of Fat Rwctot JAERU2M

9. Concluding Remarks

The homogenization code SLAROM has been revised. The present version has more cellgeometries than the first version, so almost all the cell feometries appeared in fast reactorsand critical assembles can be treated exactly. SLAROM uses the JFS type group constant setsas a basic nuclear data and moreover if users prepare their effective cross sections for eachmaterial region in the PDS file, a cell calculation can be performed starting from PATH step.The cell with double heterogeneity can be easily treated.

The main common blocks have variable dimensions. The size of blank common shouldbe set depending on a problem size. The subroutine name including blank commons are asfollows;

ESLMJ for PREP step, PATH for PATH step, P1JF for PIJF step,EDIT for EDIT step, REACTM for RATE step and EIND for EIND step.This code is included in the JAERI fast reactor neutronics calculation code system. The

output cross section on the PDS file are fed to other codes by the interface program JOINT.The code system includes the 2-, 3-D diffusion code CITATION-FBR, 2-D Sn transport codeTWOTRAN-2, 2-, 3-D diffusion perturbation code CIPER, 2-D transport perturbation codeSNPERT, 2-D burnup code PHENIX and 3-D burnup code 3DB. Users can prepare input dataand files for these codes by using JOINT. Such a procedure will be a simple way to apply theaveraged cross sections obtained by SLAROM.

Acknowledgments

We are indebted to H. Takano and Y. Ishiguro (JAERI) for their valuable commentsduring the cou.se of code development. We also thank to H. Inoue (JAIS) for his assistancein programming. M. Nakagawa wishes to express his thanks to K. Shirakata (PNC) for hissupport to the work.

JAERI1294 79

Itoforsncss

1) Nakagawa H. and Twchikadd K.: "SLAROM: A Code for Cakuktic* of a Hetcrogeaeow Core at FaitReactor", JAERI-M S916 (1974) (is Japeaeet).

2) Takano H., Hasegawa A., Nakagawa M., Wiifuro Y. and Katauagi S. : "JAERI Faat Reactor GroapConstants Set, Veniom II", JAERI 1225 (1978).

3) Takano H. and bhiguro Y. : "Production and Benchmaik Teatt of Fact Reactor Groap Coaetaat SetJFS-3-J2", JAERI-M 82-135 (1982).

4) Benoiit P.: CEA-R-2278 (1964).5) Nakagawa M., et al. : "Code Syttem for Fast Reactor Neutronict Analysfc", JAERUi 83-066 (1983)

(in Japanese).6) Twchihathi K. : "LAMP-B: A Fortran Profram Set for the Lattice Cell Analyiia by CoUitoo Probability

Method", JAERI 1259 (1979).7) Abagjan L.P., et al.: "Group Constanti for Nuclear Reactor Calculation", Couultants Bureau, New York

(1964).8) Kikuchi Y., Nariu T. and Takano H., et al.: J. Nucl. Sci. Techno!., 17(7), 567 (1980).9) Takano H.: private communication.

10) Hummel H.H. and Okrant P. : "Reactivity Coefficient! in Lane Fait Power Reecton", Americas NuclearSociety (1970).

11) Menegketti D.: ANL-7320,377 (1966).12) Takano H. and Matwl Y.: J. Nucl. Sci. Technol., 18(2), 152 (1981).13) Takeda T., at al.: J. Nucl. Sd. Technol., 18,93 (1981).14) Atai K. and TMcUhMhi K.: "A Subroutine Reading Data in Free Fomat", JAERI-M 4458 (1971) (i»

Japaneae).15) Atai K.: private communication.16) Takano H., Hategawa A. and Kaneko K.: 'TIMS-PGG: A Code Syttem for Prod«ci«g Group CoaMtaatt

in Fart Neutron Energy Region", JAERI-M 82-072 (1982).17) Blomquirt R.N., et al.: ORNL/RS1C-44 (1980).18) Mcknight R.D.: Nucl. Sci. Eng.,75, 111 (1980).19) Nithimura H. : "One-Dimensional Diffusion and Perturbation Code, SIMPLE-D (No.4)", JAERI-meaio

(published) 4381 (1971).20) ENDF/B Summary Documentation, BNL-NCS-17S41 (ENDF-201), 2nd Edition,.compaed by D. Garber,

BNL, Upton, N.Y. (1975).

SO SLAKOU: ACo»lbtO*Ho»otMlaa1lo«Cric»totioaof ftttKuctor JAEM12*4

Appendix : AuxWary Programs

1. PDSDMP

The PDSDMP code prints out all kinds of the data saved in the PDS file. It can be aboused to delete the data. The input data format is shown in the following.#1 (212)

NMFLG Assignment of input data type for nuclide code number (effectiveonly for microscopic cross section)

#2

= 0>0

IDEL » 0f 0

Character typeInteger typeNo effectDelete operation

(2(2A4,2X), 6X, 2A4) or (2(2A4,2X), 101, A4)ANAME (2)NAMEPRE (2)NUCNAM(l)KIND(l)

« ID- MACR- MICR= BSQ= KAI= FLUX

Member nameProgram nameNuclide code number of microscopic crow sectionData to be printed outID informationMacroscopic cross sectionMicroscopic cross sectionBucklingFission spectrumNeutron flux

Card #2 is repeatedly input for a number of cases. The DDNAME for PDS file is USERPDS.i The sample data is shown in Fig. A.I. When IDEL + 0, the ID data should be deleted at thei last step.

• • Nixe «•

//JCLt JOR/ / EXEC JCLt//JYtlH DO 0»T«,DLM-U»'II JUSER •l«»lXS0,IM.RMCMMM,0t31.110

OPTP miCLMS>R,MTlFV«JU»,MltWO*»>/ / EXEC F0RT77,S0>*J13S(.XMX',«->MI<WRCE.ELH<»/ / EXEC LKE»77,MtVUt'' . IMM.LIM31>

; / EXEC toIIHil* tO eSN'JMM.XSECTlM.MTA.MSMOLtlintoal DO 0»>J»S0.XIECTim.MT*.llSF«Kittsism to *SIMPLE OF MIX CO»E- 1 1 1 1SHHPL1 SLMtDH5ANPIX SLMtOH

3 1»zs i.ooo t»* I.OOO n% 1.000/>+ •

>,t*r'MT'

ooooooio X M I X M000CMM XR1XMO M M t M XHXM0«»M»H XRIXMM|MM| f mtVADv v f i f f l f -Jln&ilfivI l l l l l l l XNIICD0 0 M M 7 1 XMIKU

XMIXOOXMIXMnuxtoXRIXM

OMMMO XMIXOOXRIXMXHZXHXNIN0XNIXtOXNIXMXRIXMXRIXMXRIXMXRIX«O

FI».A.1 Sample input data for PDSDM? code.

JAERI1294 Atumiix: AMXUHJ ftotnt 1

2. MIX

The MIX code performs a mixing operation of macroscopic and microscopic crosssections. The weighted average of some macroscopic crow section sets saved in the file arecalculated and stored in the file. For the microscopic cross sections, the macroscopic crosssections are composed by weighting with atomic number densities specified by uteri.The averaged cross sections are calcniatud by the formula

where £ , » macroscopic cross section,Wt • weighting factor.

The diffusion coefficients are calculated by using the above formula or the following one,

<D> = Sura W/Sum CWCl//),)] .

The macroscopic cross sections are obtained as follows;

2« = Sum[AT • « / ] ,

where N* • atomic number density of nuclide n,

o/-microscopic cross section of reaction X, : •and the itot^pic diffusion coefficients is defined as

D = Sum [1/(3-tf« • • „ • ) ] ,

the anisotropic diffusion coefficients Dav, Dt and D± as

where Dx* is the output anisotropic diffusion coefficient when the cell calculation has beenmade, £ , r is the transport cross section calculated from the input atomic number densities,and S,r° the one calculated from the atomic number densities used in the cell calculationwhich have been written in the ID data. The input data format is described below. (Thesymbol * shows the free format.)#1 Title (18A4)#2 ( • )

#3

NMIX - N > 0= - 1

IPRTI» 0- 1

IPRTO- 0- 1

IOP* 0* 1

Number of macroscopic cross section sets to be avenged.Calculation of macroscopic cross section from microscopic one.Option of print for input data.No.Yes.Option of print for output data.No.Yes.Calculation formula of diffusion coefficient.Arithmetic average.Inverse average.

IF NMIX > 0 , the following cards are necessary.(4A4.F14.0)RNAMBX(2)CNAMEX(2)RATIO

Member name of macroscopic cross section.Program name.Weighting factor.

82 SLAROM: A Cod« fa CMnic-OjwdiKton Cilr«btin« of PMHtwctor JAEM12M

This card is repeated by NMIX times.#4 (4A4)

RNAME (2) Member name for output cross section.CNAME (2) Program name (the same as CNAMEX).IF NMIX * - l , the following cards are necessary.

#5 (4A4)RNAMEX(2) Member name of microscopic cross section.CNAMEX (2) Program name.

#6 (4A4)RNAME (2) Member name for output cross section.CNAME (2) Program name (the same as CNAMEX).

#7 (•)NMNUCL Number of nudides composing macroscopic crou section.IDIFF Option for diffusion coefficient.

- 0 Isotropic diffusion coefficient.* 1 Anisotropic diffusion coefficient.

#8 (•)(NCODE(I), DENIN(I), I - 1, NMNUCL)NCODE Code number of nuclide.DENIN Atomic number density (IOM atom/cm* unit).The sample input data is shown in Fig, A2.

//JCLS JDI MMM10 PMMP/ / EKEC JCL« MMM» PMMP.'/SYJIN DO Dm,DLM>'»*> OOMMM NtMW/ / JUSER »1HJJ5O,»*>;»«A«*.MJ,0431.110 HMMU PtttMPC.I 1.1 U.O T.O 0MOMSO n<M»OPTF HDT:FY"JI35O,PAJJ»O»O. OOOOMM nttm

II EXEC FOUTrr.SO-'JiSSO.PDSDUHP'.ft-'NOIOUItCE.EUlO}', 000*0*7* N t M P/ / •••.fo«T- nttmII EXEC LKED77,Pl«WLll.tJ0000.LIItJl1

/ / EXEC GO//USEUPDS DD DSN.J235O.XJECTION.»»T»,D1SP.OLI) 0 0 9 M 1 0 * P»»K»//SVSIK 00 • 00000110 ntMT

1 00000110SMIPL1 SL*«OH IDSAKPL1 SLAP.OM K M PMMtPSMtPLl SLUKtW MACHO PttHtPS4NPL1 SLAItOH *2tNICK0SAHPU1 ILAROtt tlSNICRDS*HPU1 SLXROM *ttMC*0/«+•

Fif.AJ[ Sunptt input data for MIX cod*.

Documents

SLAROM: A Code for Cell Homogenization Calculation of Fast