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U.A.R.A.E.E./Rep.9 <

UNITED ARAB REPUBLIC

ATOMIC ENERGY ESTABLISHMENT

REACTORS DEPARTMENT

A MULnGROUP MULTIREGION CRITICALTTY

CALCULATION DIFFUSION CODE

BY

H.Y. FOUAD and F.H. DIMITRI

1970

SCIENTIFIC INFORMATION DIVISION

ATOMIC ENERGY POST OFFICE

CAIRO, U.A.R.

C O N T E N T S

Page

A B S T R A C T i

1 . INTRODUCTION 1

2 . THEORY OF CRITICALITY CALCULATION USING THE MULTIGROUP

DIFFUSION MODEL 2

3 . NUMERICAL METHOD IN THE CRITICALITY CALCULATION 3

3 . 1 Di f ference Equations . . . . . . . . * . . , > . . , . . . . . . . 3

3 . 2 I t e r a t i v e Technique <•<> . . . . . . . . . . 4

3 . 3 Source Conversion , 5

o . 4 convergence v*nceri.an . . . . . . . . o o o « o . . o » e o o o ' o . . . . . « « o . o

4 . RESULTS SAMPLE PROBLEM . . . . . o 6

O o U vJN v L U O l U N O « . o « a « o o . o » o o o . o . . . . « « o « o o o o . o a * . « . « » » » . . o . » « . O

K £ l l ! u i V £ N U G S • • o o . . o o * . o o « . . » o « . o » o o o o . o o o « < > a . . . . o . . . . o 1 U

APPENDIX I •.••••••••••. o o 11

APPENDIX II ..o.o „... o......... o. o 12

AJfif J5N 111. JL X X X o . « . * . o « « 9 . o o « 0 . r o » . . * . o . . . « o 0 o . . « o . e o . . . . « . o . * « . 1 4

APPENDIX 1Y 21

A B S T R A C T

A multigroup, multiregion, one dimensional critical!ty calculation diffusion code was developed operational on the

I.B.M. 1130 computer. The code treats the three geometries,

i.e. slab, cylinder and spherical. A maximum o£ 18 energy groups, 4 regions and 101 space points could be handled.

1- INTRODUCTION

An important problem in reactor analysis is the criticality

calculation problem* It involves considering the balance bet­

ween the neutron generation and removal rates* Basically, this

balance has to be treated by the Boltzmann transport equation.

However, good results could be achieved by using the much sim­

pler diffusion model. The main approximation in the diffusion

model is the assumption of isotropy. If a correction is made

for the scattering angular preference, reasonably accurate

results could be obtained*

In the diffusion model, the criticality calculation prob­

lem takes the form of the eigenvalue problem, where a hunt for

the highest eigenvalue is made by iterative techniques. Since

the problem involves matrix inversion, direct inversion is

used in one dimensional problem and inner iterations has to be

used in the more complex two dimensional problems.

In this work, the one dimensional problem is handled in

the three possible geometries; namely slab cylindrical and

spherical. Provious works (1,2) handled the same problem using

the I.B.M. 1620. Computing facility* Due to its limited

memory, 4000 words, the work was limited to a four groups, four

regions model. As the I.B.M. 1130 computing facility became

available, with a memory capacity of 16,000 words the model

was extended to 18 groups, four regions and 101 points.

Since the accuracy of the results of the criticality cal­

culation is heavily .dependent on the accuracy of the group con­

stants used, the extension of the number of groups would enable

using a smaller lethargy interval per group and thus a more

accurate averaging of cross sections. Also, the finer the'

spectrum determined the more accurate the handling of energy

_ 2 -

dependent reaction rate evaluations would become, as in the

breeding and depletion calculations for example.

2- THBORY OF CRITICALI1Y CALCULATION USING

THB MULTIGROUP DIFFUSION MODEL

The group diffusion equation consider the balance between

neutron production and removal.

Neutron production has two modes:

a) Fission neutrons due to chain reaction*

b) Slowing down of neutrons from higher energy groups

due to scattering collisions*

Neutron removal has also two modes:

a) Leakage of neutrons from the volume*

b) Removal due to absorption in the material and removal

due to downscattering to lower energy groups.

Thus the multigroup diffusion equation can be written in

the form

where '

r denotes the spatial dependence,

g is the energy interval under consideration

0 neutron flux ^-T total removal from group g; — 9 Q

- y ^ + z J c o + Jrzf.oD D (r) diffusion coefficent *s5f/

2 1 transverse buckling

- 3 -

* absorption cross section,,

A down scattering from group gt to g' . y y

XL integral of fission spectrum over the energy range of g.

$ a Normalized source density

where,

// avarage number of neutrons produced per one fission 5Ha fission cross section "^ the eigenvalue of the problem which is related to the

multiplication factor*

If the group constant is to be considered constant in the same region, the general diffusion equation can be written in the form

3,0, NUMERICAL METHOD IN THK CRITICALI1Y CALCULATION

3oi Difference Equations

As described in the previous work (i,2), the laplacian operator ^ can be expanded in the general form

and using the centeral differences methods (3) we have • ~ \

( A'r)2

•• 4 «—

J2f a *n-hl ~ MB-1 (2 A r)

Using these las t 3 equation and substetuting in the general form of the diffusion equation, the difference equations can be written as,

where

°<1B = X

n

+ E ^ i o<3n . i - 2J-S1

°<2n - ^ m - H ^ a n A ( * r )

og

b , !£*}*[ a iBl(n)+ r S . tf , 1 n Dg L 9 ^ t t ' T Z _ g » g > V n J

p s 0 ,1 ,2 for a slab, cylinder or sphere

(A r) =s mesh width, constant in the same region r s distance of point n from the or ig in

3»2 I terat ive Technique:

Here we shal l l i s t the mathematical equations derived in -(1 ,2) to be used in the i t era t ive technique.

l!he difference equation ( 3 ) can be transformed into a two point equations

W l a ~ _AJUS ^ (f)

l + 8.

5 -

where

snti n * T F e ;

Ln - l - c TH

C n

rn

bn <^fn"

c*2n - 2

The interface and boundary condition have been discussed in detail in the previous work (1,2)

3.3 Source Conversion

With an initial source guess So (r ) the flux vector $ is computed, and before begining a ne^r iteration the source is recom­puted using the equations

G (rj = 21 J/ £* jf n g *—g rgn

A - o/ G (rn> d Vp

3,t:(rn) . G (rn) / ^

S^r ) = ( l + 6 t ) »ft(?B) - «t

s t" 1( rn)

Where, dVp « d r

a 2TT rdr « 47Tr dr

6 an acceleration t the iteration

for P at 0

for P=»l for P = 2

factor index

- 6 -

3.4 Convergence Criterian

The eigenvalue convergence criterion is used to terminate

the iteration process, it is given as

£ 6 x

£ is the accuracy needed and is given as input,

4- RESULTS SAMPLB PROBLEM

As a test to this code a problem of a cylindrical reactor

corewhich was given in published data was handled.

The reactor is cylindrical of two regions, the core consists

of enriched fuel contaning U2^5, U , and cooled with CQ- gas.

(Al) is used as cladding.

The second region is a block of graphite used as reflector.

This problem was treated using 15 energy groups, 2 regions and

81 space points. The reactor core has a radious of 60 cm and

the total reactor radious was 160 cm.

The input and output of this case is given in appendix IV.

Fig. (l) shows the convergence of the eigenvalue, and Pig. 2

shows the flux plots for groups 1, 5, 10 and 15.

5- CONCLUSIONS

Ohe use of multigroup model in criticality calculation have

two main advantages. 1.0. on one hand the use of multigroup :

model enables to obtain the neutron spectrum inside the reactor

in many different levels, which gives a more clear picture ©f

the spectrum.

1.010

1.005

1.000

» 0.995 0

a g 0.990 to W 0.985

0.980

0.975

0.970 T 2

T 4 3 5

T" 6 Iterations

Fig. (l): Eigenvalue Convergence.

3.0-

2 . 8 - F i g . ( 2 ) : Group F luxes .

2.4

2.2-

2.0

6

Group 15

(Thermal)

R e f l e c t o r

-i « \

11 16 21 26 31 36 41 46 51 56 61 Itadious (mesh p o i n t s )

1 r 66 71 76

- 9 -

This is more informative if a calculation is carried out

handling the energy dependent reaction rates as in the breeding

or depletion calculations for example.

2.0. on the other hand, the accurcy of the multigroup

model is affected by the use of macroscopic cross sections.

As the accuracy of these cross sections depend on the energy

interval over which averaging is made, then the higher the

number of energy groups, the smaller the energy interval over

which averaging is made and the higher the accuracy of the

multigroup method.

- 10 -

R E F E R E N C E S

H.Y. Fouad, FoH. Dimitri, nA four-groups four pegions

criticality calculation diffusion code". UAR.ABB.

Rep. 85 June 1969.

H.Y, Fouad, F,Ho Dimitri, MA two group, two-regions

criticality calculation diffusion code.* UAR.ABK.

Rep.-79 Feb, 1969.

H.Y. Fouad, F.H. Dimitri, "The use of point jacobi

iterative technique for nuclear reactor criticality

calculation"• UAR. ABB. Int/Rep, 22

H.P. Flatt, D.C. Bailer, "AIM-5, amultigroup one dimensional

diffusion equation code". NAA-SR-4694t March I960.

O.J. Harlow, M.C. Suggs, "WANDA-5-A one dimiassional

neutron diffusion equation code." WAPD-TM-241, Nov.

1960.

R.S. Varga, "Iterative Numerical Analysis", Computational

and data processing center. University of pettes-

burg, 1959.

APPENDIX -I

START

~1 Input Data!

E ^ ^ E » £ i;.» «j

Coaata&t* Calculation* KCl -+> AC8

I B_

'••I1

A

No

I Eig«nralue

I Hew Source

S(r) » 0(r) / -x

Eiganvalu« Convarganca

• !-••• I. m i — ^ M C M I — » — — — « — r — « —

y««

Print Out Part j

Stop

Pigi (a): Flow Chart of the Program.

f

- 12 -

APPENDIX II

List of Symoble Used in Program &

Corresponding Variables in Equation•

1* Symbols as Input:

A In i t i a l source guess SQ(n) M No. of regions M ( 4 N No, of mesh points N 4 101

NOG No„ of energy groups NOG ^ 18

NDS No, of groups to which there is down scatteringsl

LB Interface points in must be odd

BUCK2 Transverse buclking Bg

SIGA Macroscopic absorption cross section

SIGT Total removal cross section

DIF Diffusion coefficient D

TRANS Transfere coefficient cross section

CHI Integral of fission spectrum

VUSIG Fission cross section

BPSl Accuracy factor .

THBTA Source extropolation factor 0.

DEIR Mesh width ( A r)

R Radious measured from origin

2- Symbols Calculated; « ^ H B B t f * M H M a H « a t H C H a H « « K M M M M H M H I M i ^ M I I B M M

D ss

BETA 3

X S (r)t j f -^« g° g *V

n l i » 6 rn"1 n

- 13 -

DELTA = 6 n + 1 M X

n L 4- , n T n

PHI tf tf n

n+ 1 + Pn n

TTFS f szr

n4 1

/N EIQBN

EIGBNI

SOU

ICT MICT

Eignvalue of i t e r a t i o n t = \ a j G(r ) d V

Eigenvalue of i t e r a t i o n ( t - l ) Recomputed source

s » Q />,

Iteration index

Max Ho. of iterations

J- Control Symbols;

Nl

N2

N100

Geometry control.

=rl for a slab, p = 0

«*2 for a cylinder p s 1

= 3 for a sphere p = 2

Boundary condition control

=sl symmetric problem

«2 un symmetric problem

Iteration control

aO convergence not reached

si convergence reached

=2 max No. of iteration is used.

Index of the point by which,/the. flux; is normalized

- 14 -

APPENDIX I I I

Program Li s t ing

/ / JOB / / FOR

* LIST ALL * i0CS(CARD,U32PRINTER) *- ONE WORD INTEGERS

DIMENSION A(5),AC1(4),AC2(4),AC3(4,18),AC4(4,18),AC6(4,16), 1AC7(4,18).AC8(4,18),AC9(4),BUCK2(4,18),DELR(4),DIF(4,18),LB(4), 2SIGA(4,18),SIGT(4,18),S0P(4),CHI(4,18),VUSI0(4,18),TRANS(4,18)

DIMENSION DP(4),GP(4),G1P(4),S0PP(4), 1R(10I),FL(101),FUP(101),SOU(101),BETA(101)?DELTA(101),RI(101)?

2D(101),G(101),G1(101),SOUP(101),PHI(101,18) 1 READ ( 2 , 2 ) N1.N2,L,LG,KF1,KF2,KF3,KF4

WRITE (3 ,7023) T023 FORMAT ( l H l )

2 FORMAT ( 1 0 1 2 ) WRITE ( 3 , 5 ) N1,N2,L

5 FORMAT (51H THIS PROBLEM HAS THE FOLLOWING SPECIFICATIONS / / 1 16H GEOMETRY Nl « 1 3 / 26H BOUNDARY CONDITIONS N2 - I3 /31H FLUX 2 NORMALIZED BY POINT - 13 )

READ ( 2 , 3 ) M,N,N0G,(LB(I).I«1,M) READ ( 2 , 7 ) EPSl,THETA,R(l),(DELR(l),I-l,M) READ ( 2 , 7 ) ( (BUCK2(l ,J) , I - l f M),J- l ,N0G) READ ( 2 , 7 ) ( ( S I G A ( I , J ) , I « 1 , M ) , J « 1 , N 0 G ) READ ( 2 , 7 ) ( (DIF(I ,J ) , I«1 ,M) ,J .1 ,N0G) READ ( 2 , 7 ) ((TRANS(l ,J) ,I- l tM),J. l ,NOG) READ ( 2 , 7 ) ( (CHI(I ,J ) , I .1 ,M) ,J-1 ,N0G) READ ( 2 , 7 ) ( ( V U S I G ( I , J ) , I . 1 , M ) , J « 1 , N 0 G ) READ ( 2 , 7 ) (A(I) ,I-1 ,M),EFF WRITE (3 ,7008) N0G,M,N,(LB(l). 1.1,M) WRITE (3 ,7009) EPS1,THETA,R(l),(DELR(l),I-1,M) CALL DATSW ( l , IFA) IF( lFA-l ) 7101,7101,7102

7102 CONTINUE DO 8005 I«1,N0G WRITE (3 ,7002) I WRITE (3 ,7003) (SIGA(J , l ) , J« l ,U) WRITE (3 ,7004) ( DIF(J,J) ,J«1,M) WRITE (3,7005MTRANS(j , l ) ,J» | fM) WRITE (3 ,7006) ( CHl ( j , I ) . J« l ,M) WRITE (3 ,7007) ( V U S I G ( J , I ) , J « 1 , M )

8005 CONTINUE 7002 FORMAT (2lH DATA FOR GROUP I2/26X, 8HREGI0N 1,12X,8HREGI0N 2,

112I,8HREGI0N 3 , 1 2 1 , 8H REG I ON 4 )

- 15 -

7003 FORMAT (20H ABSORPTION COEFF, 4(2X,E16.8,2X) 7004 FORMAT (20H DIFFUSION COEFF , 4(2X,E16.8,2X) 7005 FORMAT (20H TRANSFERS COEFF , 4(2X,E16.8,2X' 7006 FORMAT (20H CHI , 4(2X,E16.8,2l" 7007 FOR^f (20H NU SIGMA FISSION, 4(2X,E16.8 ,2X, , 7008 FORMAT (23H NO. OF GROUPS NOG - I5/23H NO. OF REGIONS M -15

1/23H NO. OF POINTS N -I5/25H INTERFACE POINTS LB-I5,3I5) 7009 FORMAT (32H CONVERGENCE CRITERION IF SI -E16.8/32H EXTRAPOUT

HON FACTOR THETA - E l 6 . 8 / 1 OB R ( l ) -E16.8/10H DELR -E16.8,3E16 2 .8 )

3 FORMAT (615) 7 FORMAT (5E16.8)

7101 CONTINUE WRITE ( 3 , 7 0 2 0 )

7020 F0RMAT(//37H ICT EIGEN EIGN1 ) NM1-N-1 MM1-M-1 LB1«1 BO 520 I-1,M LB2-LB(l) BO 522 J«LB1,LB2 SOU(J).A(I)

522 CONTINUE IF(LB2-N) 521,520,520

521 SOP(l) « A(I+1) LB1-LB2+1

520 CONTINUE LB 1-2 BO 265 I«1,M LB2»LB(l) BO 255 J.LB1,LB2 R(J)»R(J-I)+DELR(I)

255 CONTINUE LB1-LB2+1

265 CONTINUE BO 318 I-1,N0G BO 318 J-1,M SIGT(J,I) - SIGA(J,l)+TRANS(J,l)+DIF(J,l)*BUCK2(J,l)

318 CONTINUE GO TO (81,82,83),N1

81 BO 84 I-1,N Rl(l) . 1.0

84 CONTINUE P-0.0 PBI - 1.0 GO TO n

82 BO 86 I -l.N Rl(l) -R(l)

- 16 -

66 CONTINUE P - 1 . 0

PTM • 6.2831853 GO TO 91

83 DO 87 1.1 ,N RI(I ) . R ( l ) * R ( l )

87 CONTINUE P - 2 . 0 PIM • 12.566371

91 DO 92-I«l ,M ACI(I)JE*DELR(I)

92 CONTINUE LB 1=1 LB2-LB(l) DO 120 I«2,NM1 FAC2«AC1(LB1)/R(I) FIP(l)«1.0/(l*0+PAC2/2o0) FL(l).FAC2*FIP(l) IP (I-LB2) 120,110,110

110 LB1-LB1+1 LB2»LB(LBl) FAC2.AC1(LB1)/R(I) AC2(LBl-l)^1.0/(loO+PAC2/2.0) ACl(LBl-l)«FAC2*AC2(lBl-l)

120 CONTINUE DO 135 J«1,N0G DO 135 1=1,M AC3(I,J)«(DELR(I)**2)/DIF(I,J)

AC4(l,J)«AC3(l,J)*SIGT(l,j) 135 CONTINUE

GO TO (l4l,l5l),N2 141 DO 145 J»1,N0G

AC6(1,J)»AC3(1,J)/(2.0^(1.04P)) AC6(2,J)«SIGT(l,j)#AC6(l,J)

145 CONTINUE GO TO 175

151 DO 154 J«1,N0G AC6(l,j)«A(M(l,J)*FI*f2)-FL(2)+1.0 AC6(2,J)-AC3(1,J>PIP(2)

154 CONTINUE 175 NM2-N-2

DO 195 J-1,N0G DO 195 I-1,NM1 AC7(I,J)«AC2(I)*AC4(I+1,J)-.AC1(I) AC8(I,J)-AC2(I)^AC3(I-»-l,j)

195 CONTINUE ICT.O MICT-50 EIGIN.0.0

- 17 -

EIGN1-0.0 130 LOB-2

BO 160 I-1,N0G K8-1 K9-LB(l) DO 114 J-1,N D( J)«CHI(K8, l)*S0U( j) IP (J-K9) 114,13,13

13 IF(J-N) 140,114,114 140 BP(K8)-CHl(K8+l,l)#S0P(R8)

K8-K8+1 K9-LB(K8)

114 CONTINUE IF(l-l) 61,61,22

22 LB3-I-1 DO 24 J-1,MM1 I1*LB(J) BP(j).llP(j)+TmNS(J+l,LB3)^PHl(ll,LB3)

24 CONTINUE I2-LB(l)+l 13-1 DO 40 J«1,N IF(J-I2) 30,128,128

128 I3.I3+1 I2«LB(I3)+1

30 D(J)«D(J)+TRANS(I3,LB3)*PHI(J,LB3) 40 CONTINUE 61 60 TO (60,65),N2 60 BETA(1)«AC6(1,I)*D(1)

DELTA(2)-AC6(2,I) GO TO 75

65 BETA(2)«AC6(2,l)*D(2) DELTA(3)-AC6(l,l) L0B.3

75 I6-LB(l) 17.1 DO 90 J-L0B.NM1 SM«AC3(l7, i W J)*F1P( J) CK«AC4(I7,I)*FIP(J)-FL(J) CI«FL(J) SL-l.O-CL C0N1-1,0/( 1 •p+DELTA( J) ) IF (J-16) 80,85,80

80 BETA(J)-SI^GONI^BETA(J-I)+SM m^TA^S+i )«C*+C0N1*(DELTA( J)+CL) m ,T0.V 90

B5 „Gp-aCltM)

- 18 -

SMP*AC8(l7 I W D P C I 7 ) GAM»((DIF(I7+1,I)#DELR(I7))/(BIF(I7,I)^I>1SLR(I7+I)))-1.0 GAMloGAM+1.0 ' CON2*0»o# (CK+DELTA( J )#CON 1*2.0+CKP+CL*CON 1 l+(GAM+CIP)*(CKP+2.0)/SLP)

C0N3»U0-CLP/2«0 BETA(j)-(SM+C0Nl^(2o0~CL)^BlSTA(J-l)+GAMl^SMP/SU?)^(StP/(GJUIl^(2.0 1-ClP))) DELTA( J+l)«( C0N2*SU»-GAM*C0N3-CIp/2 . 0 )/( GAM1* CONS ) I7.17+1 I6-LB(I7)

90 CONTINUE PHl(N,l)»OcO DO 345 J«1,NM2 I20.N-J PHI(I20,I)-(PHI(I20+1,I)+BETA(I20))/(1.0+DELTA(I20+1))

345 CONTINUE GO TO (155,152),N2

155 PHI(1,I)«PHI(2(2,I)^BETA(1))/(1.0+DELTA(2)) GO TO 160

152 PHl(l,l)»O„0 160 CONTINUE

LB2*LB(l) M80«l DO 10 1=1,N G(I)«O0O D097 J»1,N0G G(l)«G(l)+VUSIG(M80,j)KPHl(l,j)

97 CONTINUE G l ( l ) . G ( l ) * R l ( l ) IP (I-LB2) 1 0 , 6 , 6

6 IP (I-N) 8 ,10 ,10 8 GP(M80)«0o0

DO 9 J=1,N0G GP(M80)-GP(M80)+VUSIG(M80+1,J)^PHI(I,J)

9 CONTINUE GiP(M80)«GP(H80)#Rl(l) M80-M80+1 LB2«LB(M80)

10 CONTINUE M80-1 LB2-3 LB3-LB(l) EIG1S-0.0

27 SUM.0.0 DO 28 I-LB2,LB3,2 IP (I-LB2) 273,273,277

273 IP ( 1 - 3 ) 277,277,275 275 S0».SDII^GIP(M8O)+4.OKG1(I-1)+Gl(i)

- 10 -

M80-M80+1 GO TO 28

277 SUM-SUM+Gl(l-2)+4.0^Gl(l-l)+Gl(l) 28 CONTINUE

AC9(M80)=(SUM*DELR(M80) )/3.0 EIGEN-EIGEN+AC9(M80) IF (M80-M) 29,295,295

29 LB2-LBQ+2 K80-M80+1 LB3-LB(K80) GO TO 27

295 EIGEN«EIGEN*PIM 0016 I-1,N SOUP(I).G(I)/EIGEN

16 CONTINUE ICT-ICT+1 D037 I»1,MM1 S Q P P ( I ) « G P ( I ) / B I G E N

37 CONTINUE ERROIUABS(EIGEN-EIGNi )/EIGEN IF(EMtOR-EPSl) 18 ,18 ,41

18 N100-1 GO TO 33

41 IF(ICT-MICT) 4 2 , 4 2 , 3 1 42 N100»0

IF(lCT-2) 215,215,53 53 FAC-THETA+1.0

DO 2224 1=1,N SOU( I) .SOUP (I )*FAC-THETA*S0U( I)

2224 CONTINUE DO 245 I~1,MM1 SOP( I )«SGPP( I )#FAC-THETA*S0P( I)

245 CONTINUE EIGN1-EIGEN GO TO 33

33 IF(MICT) 18,18,315 315 N100.2

GO TO 33 215 DO 220 1=1,N

SOU(l)-SOUP(l) 220 CONTINUE

DO 225 1-1,1011 SOP(l)«SOKP(l) SOP(l)-SOPP(l)

225 CONTINUE EIGN1-EIGEN

33 WR1TE(3,77)N100,ICT,EIGEN,EIGN1 IF(N10QT;1) 130,170,3$©

170 IF(EIGEN-EFF) 1130,1130,1326

- 20 -

1130 WRITEf3 113l) 1131 F0HMAT(38H EIGENVAL IS LESS THAN MINIMUM KEFF )

GO TO 320 32 WRITE(3,19) 19 F0RMAT(36H MAXIMUM NO. OF ITERATIONS EXCEEDED ) 320 WRITE(3,77) N100, ICT,EIGEN,EIGN1 77 F0RMAT(2I5,2E16.8)

PHIC«PHl(L,LG) D01175 I«1,N0G D01175 J-1,N PHl(J,l)-PHl(J,l)/PHIC

1175 CONTINUE WRITE(3,702l) KF1,KF2,KF3,KF4 DO 20 J«1,N WRITE(3,7022) R(j) ,SOU(j),PHl( J,KFl),PHl(J,KF2),PHl(J,KF3),PHl( J,

1KF4) 20 CONTINUE

7021 FORMAT(//5X,7HRADIOUS,9X,6HSOURCE,20X,18HN0RMALIZED FLUXES / 13 7X, 5HGR0UPI2, 9X, 5H GROUP 12,9X, 5HGR0UPI2, 9X, 5H GROUP 12 )

7022 FORMAT (6EI608 ) CALL DATSW (0,IFH) IF ( iFH- l ) 7011,7011,1

7011 CONTINUE CALL EXIT END

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APPENDIX IV

Program Input/Output

Input s

The program input data contains the following cards t

(1) The let card to identify the type of the problems it contains,

Nl The problem shape

* 1 for a slab

- 2 for a cylinder

- 3 for a sphere

N2 The problem type

- 1 for symmetric problem

» 2 for un-symmetric problem

L The point index by which the flux rector is normalised

LG The group index by which the flux rector is normalised

KF1, KF2, KF3, KF4

The group numbers for which the flux is to be printed

(2) The 2nd card to give the problem dimensions

If The number of regions If 4

N The number of space points N 101

K06 The number of energy groups NOG ^ 18

LB(l) The interface point numbers, must be odd

11 ralues are intered here in assending order, and LB(lf) must

coincide with N.

(3) This card contains

H>SI The cpnrergence criterion £

THETA The extrapolation factor 0

R(l) The radious of 1st space point•

DEIR(l) Mesh width of each region, II ralues* » *i •?

(4) This card contains the ralues of the transversa buckling (BUCKS)

IffNOG falues are inered each 5 of them on one card.

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(5) The macroscopic absorption cws0 (SIGA), MXNOG values are intered,

each 5 of them on one carde

(6) The dif fusion coe f f i c i en t s (DIF) in the same format,

(7) The down scattering cross-sect ion (TRANS).

(8) The integral of f i s s i o n neutrons per group (CHl)«

(9) The j /£ f (VU5IG) values ,

(10) This card contains the intial source guess, A(l) constant per

region, M values, and the eigenvalue to be searched for*

Output :

The program output consist of two main parts s

(a) The input printing s

In this portion all the input to the program is printed, if the data

switch No.l is off o If this switch is put on this portion is not printed.

(b) The results printing :

In this portion the following is printed for each iteration,

N100 Control of convergence

m 0 convergence not reached

m l convergence is reached

ICT The iteration number

EIGEN The eigenvalue of this iteration

EIGNI The eigenvalue of the previous iteration

After the convergence is reach a table is printed containing for each

space point, ' "-

R(j) the radious at the point J*

SOU(j) the new source at this point

PHl(j,KFl) the normalized flux of point J and group KF1

PHI(J,KF2) w M » M W H W W K P 2

PHI(J,KF3) w w M H M W M W K P 3

PHI(J,KP4) " " " " « »' « »» KP4