IBD-1 : two dimensional, multigroup neutron diffusion code

TÜRKİYE

A T O M

ENERJİSİ KURUMU

ÇEKMECE NÜKLEER ARAŞTIfcMA VS EĞİTİM MERKEZİ

Araştırma Raporu No: 233

IBD— 1 : TWO DIMENSIONAL,

MULTIGROUP

NEUTRON DIFFUSION

CODE

Ulvi ADALIOĞLU,

Raşıt

TUNCEL

Nuclear Engineering

Department

October 1985

TÜRKİYE ATOM ENERJİSİ KOLUMU

Ç E K M S İ E M f l K L H K A H ^ . R M A :/K SCtTlf* HERKEZİ

Araştınna Raporu N o: 233

IBD— 1 : TWO DIMENSIONAL, M ULTIGROUP NEUTRON DIFFUSION

CODE

Ulvi

ADALIOĞLU,

Raşit

TUNCEL

Nuclear Engineering Department

October 1985

CÖBYKM*

1. INTRODUCTION 1 2. THEORY 2 2.1“ Diffusion equations 2 2.2- Matrix formulation 3 3. SOLUTION TECHNIQUE 7 3.1- Matrix partitioning 7

3*2“ Inner iteration problem 9

3.3“ Estimation of parameter 12

3*4“ Outer iteration 14

4. PROGRAMME DESCRIPTION 14

4*1“ Subprogrammes 14

4*2“ Yariables and parameters 15

4.3~ Input data deok and formats 16

5. APPLICATION AID RESULTS 17

RSJERSNGES 18

APPENDICES

Appendix A- Flow chart of IBD-1 20

Appendix B- The factorisation of symmetric matrices 21

Appendix C~ The square root method 22

Appendix D“ Programme listing 23

TABLES

Table 1- The ooeffioientst a,bto,d, and e at the

nodal point (l»j) 19

FIGURES

Fig. 1- Mesh structure in cylindrical geometry 4

Fig. 2- Numbering of mesh points on mesh structure 5

Pig* 3“ Ordering of mesh points for one line

partitioning 7

SUMMARY

IBD-1 : TWO DIMENSIONALfMULTI3R0UP NEUTRON DIFFUSION CODE

The code IBD written in Çekmece is used to solve two dimensional few group neutron diffusion equations. Liebman and Chebyshev techniques accelarates the solution in the inner and outer iterations of the prog­ ramme, respectively.

The so-oalled block successive overrelaxation method is utilized to improve the convergence of inner iteration of the programme. A one line successive overrelaxation, simplest case of block overrelaxation technique, is applied to the IBD code.

ÖZET

IBD-1 : ÎKİ BOYUTLU, ÇOK ORUPLU NÖTRON DÎFÜZYON KODU

ÇBAEM’de yazılmış olan IBD kodu iki boyutlu çok gruplu nötron di füzyon denklemlerini çözmekte kullanılmaktadır. Programdaki iç ve dış it eras y onları Liebman ve Chebyshev metodları hızlandırmaktadır.

Programın iç iterasyommun yakınsamasını geliştirmek üzere "ar­ dışık blok o ve r re 1 aks asy on" metodundan faydalanılmıştır. Bu metodun en basiti,bir satır ardışık overrelaksasyon IBD koduna tatbik edilmiştir.

1

INTRODUCTION

The code IBD was written to solve two dimensional few group neutron diffusion equation (l). It uses forward elimination backward substitution method for the solution of finite difference equation* Inner and outer iterations utilizes Liebman and Chebyshev accelera­ tion techniques for the flux and source acceleration respectively.

With these features IBD has limited capability to handle the problems with respect to their sizes. It seems that inner iteration is rather slow.

In order to remedy this the so-called ’'block successive over- relaxation” method is widely used. The coefficient matrix of the mat­ rix equation of elliptic difference equation can be partitioned by considering some mesh points of a particular region as a block. For instance one can take all mesh points of a horizontal mesh line or all points of adjacent two or three lines as a block. Then the new method, which is called Successive Line Overrelaxation Method, was proved to be asymptotically faster than point overrelaxation and nume­ rically very stable with respect to rounding errors (2).

This report describes a one line successive overrelaxation technique for the inner iteration accelaration of code IBD • The outer iteration utilizises Chebyshev source accelaration.

2

THEORY

2 .1

— IHffusxon equation®

The two dimension?;,. , multi group d i i*f ;ıvı i on »'inalı5ns to he solved are

+ f

2

. V +

<p*tr)

1

U|*1

J

*

^

[v

4^ct> *

i

^ I

p

) 4>k(c)

(

₂

.

₁

)

k*1

H

1*1

when

0 is the

maximum number of energy groups,

0^ (?) : the neutron flux in group g at point r ,

D® (r) : diffusion coefficient in group g at point r ,

: macroscopic absorption cross section in group g

at point r ,

: macroscopic

f

i s s

\cn

cro ss

section in

«croup

g

a t

point t ,

: scfccroscopic fission cro* < section

ire*» group g

into group h at point r F

: average number cf neutron released gy a fistic» in energy group g »

the integral of fission spectrum over the energy group

the multiplication factor.

The boundary conditions are either

*

+ B*(r) <J>^c)

a

o

for free surfaces, or

v 4

>

f(c)

=o

for the points where the geometrical and medium are symmetrical. The coefficients

(2.2) correspond to

A*(c) s i * .

0.71

B * ( D a 1

(2 3)

materiel properties of the A e (r) and B g (r) in Kq.

(

2

-«

2.2 - Matrix formulation

Defining a mesh structure in cylindrical or planar geometry one can easily obtain a five point finite difference representation of Eqs. (2.l) • The boundaries of a volume element around a nodal point (i,j) are defined by the distances, for cylindirical geometry

* 1 ** Z, . A l , z i - V

1

N j- = 2,3,

+ AIL).

, n

(2.5)

-3-and the nodal çoin. (i,

,1

}

is

& , %

t

t - t

oenter of sfc*. vc

i m *

The mesh e frn o tu re ;.s sierra i?i Fr.g«, I«

Fig. 1 - Mesh structure in cylindrical geometry

The finite difference form of the diffusion equation, Iqs. (2.l)

İ8 where

-•>»

4

^

+

4

4

$

- 4

€ , 4

-

4

^ - ' ' e u f t *

-

^

S f i i + S .r

4

# ’

V;,

«T

S f ‘4 = £

L f

V,4

-4-c>.

bt4

U - 0

(i-Jtx)

S H

=

2

L

^»‘4

^ 4

^4

and the volume element ¥,. around the nodal point (i, j) is

J*

V-J

\

1

for cylindrical geometry

Axj • AY; • l for plane geometry

(2-8)

The coefficients, a,b,c,d,e »ad the fonts of Eqs. (2.6) at boundaries are given in Ref. ( l ) in detail. Table 1 reproduces expressions of the coefficients a,b,o,d,e.

In order to represent this system of equation, that is Eqs.

(2.6) in a matrix form we need to order the equations and unknowns in some specific way (3). For instance we renumber the mesh points on mesh structure from 1 to MH consecutively by rows as shown in Fig.2,

(M-*)N+JL

N*

:m-*)n

+2

2

N

+2

N

+2

2

HH-t HR

3«-f

İN-1

-3*

2R

that the k- th equ»tSon and unknown correspoxi to he fixit*

&

c,t

tbf»(

at>i-;al

oo

1

ot

tf.

xad^x k

it j

respectively* Then the matrix xVrra x? aqe* (lx 6) Tor- group g is The

equation a&4 rnctxwns for group

4

-•«-» be or&ars.? s??ols

difference equation aad the w

~ ° ^

| » f,2,...., <5

U4)

where

4>’ T - [ t f

^ V !

S*T- [s* S

*....s*,--slj

u*

k % «

(240)

8

The SOI by Ml coefficient .«atix z m A arc iri-s-iuoible Stielt—

g

jes

xatrices

and

inverse

of

each

A has all

positive entries* i f

c.

•

“1

^

A ) 0 « Mcr^ver A a are consintently ordered, *x \t\% 2~ cyclic

g g

irreducible and diagonally dominant ' •;«}••' .jeu matrices (2>,*4)»

-6-3 SOLUTION TECHNIQUE

The solutions of Eqs* (2.6) had been obtained by inner and outer iterations (2). Outer iteration uses Chebyshev accelaration technique for source iteration whereas Liebman accelaration was utilised for inner iteration.

In order to improve the convergence for the inner iteration, one need to partition the matrix A to get block matrices for the

g

application of faster methods, i.e, successive block overrelaxation techniques.

3.1 - Matrix partitioning

By grouping mesh points shown in Pig. 2. in certain ways one can easily partition matrices A s ._g

A particular grouping of mesh points comes from considering all mesh points of a horizontal line as a block. For example consider the ordering of mesh points in Pig. 3*

H

J-A

1 t 3 % 9 »-3 i n-1 1 I I i 1 1 f 1 t 1 1 1 | 1 1 i 1 1 1 > : 1 l 1 I i 1 3 ! 1 I ! 1 I 1 k 1 I 1 1 1 % 1 . 1 i 1 , 1 • : 1 1 1 *t-3 i 1 t 1 i 1 İ - İ 1 i I 1 1 1 H-1 l 1 ) Î 1 ■ 1 t 3 % S’ N-3 •İ-İ Î z 3 ~k 9 n-3 «-a i 1 3 İ Î »-3 N-2 i4*f 1

l

where

-Each matrix B is as irreducıali tridiagonal Stieltjes matrix. Its nonzero off-diagonal entries give the coupling of a mesh point with its immediate neighbor on the same horizontal line.

%

%

The matrices D" s and E" s are diagonal and they represent the coupling of a mesh point to the mesh points of the lines above and below respectively.

3.2 - Inner iteration problem

1

The inner iteration problem is to following equations for constant souroe

find the solutions of the term

where

-9-The success3 ' o-<rzvr*s a x p sio*-- method ca1;. ftpp) vtci to Bqe. (3 * 3 / ta eiva equations

4 T

’ = ^ [ $ » ‘ - L

4

T

" j

-

9

:

$(m~i)

(S3j i « 1 , Z , . . . j H *s I * -t, * * * - > ö

where index m is the number of iteration, h) is the optimum

D

overrelaxation factor (

4

).

Eqs. (

3

.

5

) can he normalized in order to reduce the number of arithmetic operations in the following wuy % Omitting index g, let

B, = ST. £>..

(3.6)

be the factorization of B j matrices (See Appen. B) and let R. .

i

ip.

be the diagonal matrix whose non—zero elements are the diagonal entries of S .. i.e,

1,1*

( S j

İZ

O

(

3

.?;

O

(Sy) and

1

:

(**»)

Y*

-t"0

_{(i.2 a)}

1 0

-then Eqs. (3*5) become

where

where (3.9)

N i,i Yi<m> = - N;^., Yj!."' - N ;/ui Y u * ’1) + S i

V‘m) - Ub[y;w -Y > -° ] ♦ Y,'

l s | {2,

i rti ^ 1

(«-()

(»

1

)

(3.(0)

H l,o - % , M

+ 1

ss 0 •

The factorization of % fi is a t

Kli.i « -Siji

> or

-1

S i , i * «5 ^

(3.11)

(3.U)

SSi,i

has unit diagonal entries. Representing the RHS of Eqs. by the matrix equation

^>,iY;Cm

) = Ft

(5.(3)

3«?» - %etiî3ati-5î» ot

-:*.r

**-’•

•

*

t.

jv (*)

The VMS g? f acce o : vo -:-vet: ^

1

.a>-^-iiu • »eVood need ı n ,?e >d esti— »ate r»f the a peer,ra,' radivs of

8

au»s~Se

2

Sel Herat:.e» f.utîr*.f If ^ is the Oa?ısî»--3eida3 iteration watri* then the vaIvn ot spectral radi— us of is give» h,y the following theorem (Fef«.

2

, p B

283

and Ref. 3» P. 54 )

Theorem - Let A be an irreducible^ consistently ordered 2 — cyclic Stieltjes matrix and be The associated Oauss-Seidel iteration matrix. Then

Ytm>=

l t

Y‘"'°

t**»

I" y ( m ) yCm)J

J y (®î y<m-fJj

(s.iy)

lint

** ^ (£.f)

Moreover if the i-th component of and if, for ^ ® “1 ^ ^

0

•dyn) ^ ss **VUi -i ı^tns-ı] 3 (m.) A 3s ntax i *1 tm-<) is denoted by

(3.^)

U.i?)

—12'

then

\ w * ? ( * , ) * V " "

-X 1”" » A 1™ 1 » x im)

Lm. V

’ 1

- tim A'"’ = 9 ( £ J <>•«)

_ NM _ ^

How one can define several estimates of U) as follows

7i <m>

-Ul

w f r :

m

(w) T Cm)

₁

_{+ f T - x (m)k}

(

3

.

19

)

(3.20)

The iteration procedure defined by Eqs. (3.14 and 3*15) can

he

used

to determine

^ ^) • The upper \

lower bounds of A are

defined by Eqs.(

3*16

and 3.17). The right hand side of Eqs. (3.14) can be easily obtained by taking sf * 0 and W « l in Eae. (3.!>)

x

b

The inner iterations continue until w «. 1Ş s or

(

3

.

11

)

»13-3*4 — vu'sc-f iteration

Afww

7

oi?t;-ip

;■

4

f ' î * a t ' , ; Ch&hy&hey ac.-;e.la r a t ion o.re

used

fo r

fission source acc$la'<ct.o n , The f'srion t*-: t tree 5^ i* A'qs.C

3

*ş) or S in Bqa. C

3

*

9

) is aocelarated i-ftt-r <secb sweep of plane, before entering new inner iteration calculations for î&o s line of Bqs.

( 3 . 3 ) o r lq®« (3*13)-» The a lg o r it t e n u se d ar® g iv e n

in

R ef* ( l ) *

4

. PROGRAMME HESCRIPTIOS

4#1 - Subprcgraaaes

The ©ode

IBB has

the

following

subprogrammes

MAIM

PROGRAMS

Calculates

the coefficients of five point finite,differen­

ce

equation and does

power

iteration and Che

bye

her source acceleration*

OKU % Reads input data*

FİSTO : Calculates

fission

source for

flux.

QARTI : Calculates importance function.

FISTAD : Calculates fission source for

adjoint

flux TURU : Establishes matrices R,

D,

1

SACAD % Calculates scattering source term for adjoint flux HIE s Calculates optimum overrelaxstion factor, &*b.

COZZ ; Solves flaw dish/;butiea by using one lir».e acceleration techniques• SSI SRI

FSP

mm

squ

: Establishes

the,

»etrsce.-ı I

s Finds tb r îsa tric a s

i

,x

: Calculatoo the prou of

4*j

'*»3 M

: C&3 col atec tha product r*f i 3.

İ f İ 1

: Applies the Square loot method foi H . I. -■ P„ equation

i,t i 3 *

the solution of

-14-PAT s Calculates the integrals in k . ef MA XX : Calculates A and \ .

Sil : Does tbe faotorisatj.cu) of Symmetr-c Matrices

KATSA : Sets up the matrices M , S ' , 1 for whole grid and i #i i,i i,i

energy groups.

KAYÎj : Calculates the sum of scattering and fission source term

4.2- Variables and paramaters

Epsa : Convergence criterion for k and fission source. EPS3 : Convergence criterion for flux.

IB : Number of regions.

IG10 s si for flux calculations for cylindrical geometry /4l for flux calculations for cartesian geometry

İCAP _{I CAP calculations in cartesian geometry}

ICEY : ICET ^lj ’’whole core”

ICAP sljfor flux calculations in cartesian geometry ICEY i i K lf core" (s3rffi®*^rical J-axis) î or "whole

F core" in cylindrical geometry

IAD

ICAP ^llfor flux calculations in cartesian geometry ("Half core" (Symmetrical to x-axis)

XCJliT sİ J

ICAP rllfor flux calculations in a quarter core in

IC^Y J car^esiaja geometry, or, flux calculations in half ~ oore in cylindrical geometry

: - 0 for flux and adjoint flux calculations. ^ 2 for flux calculation only.

IGUC : — 1 for both power and source distribution calculation IBAK : — 1 for calculations done by using B z in x-y geometry 2

^ 1 cylindrical geometry

KMAx : Number of groups

IMAx : Number of mesh points at x or r direction JMAx : Number of mesh points at y or z direction K0MSA : Number of compositions.

IBIS

î a 0 for relative f3ö>: cvlculati»/!?

/4 0 f o r r e l a t i v e f3 an and norm al L»ed f l u x

151 ( l )

i

ffumVr o f I s f t r ic e o f ref.:wt*, I 1r= >; o r

r

d sre c tic -n .

15 2 ( l )

* lumber o f rrg n t aid*

X lit x o r r d ir e c t io n

İSİ

( i )

î Humber

o f "

ocv

I

cm

sxd* o f

r^grion

I m y o r

I direction. JS

2

(1) t Humber of '%cp

_{s id e of}

region I m ;f or

2

. direction. KK(lt)tIMAT(l)slumber of region K and number of

composition

K. DELHI (I) DELZ

( j )

x(K) xRU(K,S) d p(k,h) SA (K#I) SP (K,I) SS (K#M,E) HTUK

: The length of mesh interval 2», region I at x or r direction

_I

» 1,2,..». - fiMAx.

t The length of mesh interval in region

_J

at y or z direction «î » , JMtx.

s fission neutron fraction for £ th group

: Humber of fission neutrons for

E

th group and M th composition

: Diffusion coefficient for I th group and I th composition s Absorption cross-section for 1th group and II th composition $ Fission cross-sect ion for *C th group and H th composition t Scattering cross-section from K th to M t h group

for X th composition.

: for IGUC s 1 Thermal power of reactor in w a t t s , IGÖG

^ .1

So need for P .

s Height of reactor core for x~y geometry in cm.

4-3- Input Data Deck and

Formats-Input

data

and their formats s k ^i^ere beî c*»

Variable

Format

EPS2,

EPS

3 2

no.?

IB #

ICAP/IGEO

,

IAÛ

, IG&J, IBAST, I.;E*'»

-'3Ux,

1213

IMAx,

_{İKAxt EOKSA, IB IS}

(ISI (I), I52(X), J3S(1), 3«1,13)

(DELHI(I), I -

1

, IMAx)

8

F 10.5 (DELZÛ (1), I - 1,JMAx)

8

F 10.5 (x(K), K »

1

, KMAx)

₈

F 10.5 xN(k,n n), d p(k.s n),s a(k,n n),s p(k,n n),

8

F

10

.? (SS(K,N,NN),N a*,XMAx) P _{E 14.7} HYUK _{E 14.7}

5. APPLICATION AND RESULTS

TR-2 small core configuration, shown in Fig. 4» has been considered for criticality calculations. The control rod BC-2 is inserted while the other three rods are out of core for this calculation.

A dry irradiation tube is placed at the right side of the core. Core is reflected by Berillium blocks from one side, and the other side

Mater Be Be Be Be 8S-1 bs-2 Bc-1 D f &C-2 A1 A1 Be * Berillium blocks DİT î dry irradiation tube

BC : control rods and elements

„i î Aluminium blocks Others are standart fuel

elements

has two Aluminium bleakc Located euoh eo «&•<*>*,

Fbor (P^oufe x~y geom etry o ^ l^ 'c l^ v to a .i»a <

rîiwea % m u lt i p i i c a t less

factor

of

1*04932? for & 2 â > 2 9 oc.i&t t- svcuntwe* Tfca numfeer of compositions 3e 11 whereas

56

reflows tit**» -?wed m modelling of sxtm.es- tor core.

Total number of inner iterations for ts2?î problem 'by IBS-1 code is 880» On the contrary

1830

inner iteration» are necessary to 4®

the s«ae calculations by IBB code*

O th er

applications have proved that

a r e a l

refect

l e n t

feat is almost ^

50

* is inner iteration number ha* been achieved* But the only difficulty is to go to larger number

of

ia®eh sises

s in c e

it requires larger fast memory capacities*

:!!fi!L! . B

(1) H* fuaşel, U* Adalıoğlu, “Code IBB - A Two Dimensional* Multigroup Neutron Diffusion Code", ÇHA0J-B-19O? 1978*

(2) B* S* ?arga, “Matrix Iterative Analysis'*, Prentice Hall, 1962# (

3

) L# A* Hagemaa, "Numerical Methods and Techniques used in the

Two-Dimensional Neutron Diffusion Program PD%~5", WAPD ~ TM -

364

, Peb.

1963

.

(

4

) B* A* Hageman, "Block Iterative Methods for Two (frolic Matrix Equations with Speoial Application to the Numerical Solution of the Second-Order Self-Adjoint Elliptic Partial 3lf.tQien.tial Equation in Twe Dimensions’"«. ^APD - 1M - '21» Apr.»

-ı9-Appendix A~ Flow clmrfc ©f IBD-i

MAIH PBCCSAK

-20-Appendix B— The Jfectorisation of Symmetric Matrices (2)

Theorem 2*1 - Let 1 - (ap i) Be an N x N symn^t ^ j c positive definite matrix* There r x : r a real upper triangular matrix S s (sj^j) Pith pcs it i iiarena! entries such that

A s S T S ( B . l )

where the elements s a ^ are riven h,y

(8.1)

İ

< i

0

Appendix C- fhe Square Root Method (~î)

A direct method for the

b o

L

u î

-

oû

cf t'-<* wfc irix equation

A X : ? (C.l)

can be defined as follows, wher« A in cm f x M symmetric positive definite matrix, X and ? are the unknown and source vectors, respectively .

If A is factorized as given in Appen. B then

(C.

2

)

Define a new set of equations to be solved as

S X s T

S T ! : p (C*

3

)

The solution of Esjs. (C.3) are given directly by

i>1

U N

(0.4)

where xx

s ,

y^

s

and t\

** crt. the e n tr ie s o f

vectors

X , ! asd F,

respectively.

If the entries c x t \ x. ' • >,» * are unity tnen she number of arithmetic operations is reduced considerable

Appendix B— Prograıeme listing

ANA PROGRAM

DIMENSION SNSL'-.,2-/ ?*, 24/, £31

?*». 24, 24. FR(4, 29. 24 2« ' , SNİ < 4, 29,

.114, 2-> =S •

'

4. 24 29), t

X

( 4, 24. 29 /, V /.I i

4, 24, 29 ;

DIMENSION A(4:

24, 29) .

B<4, 29, 29), C(4, 24, 29) -

D (&

■

24, 29 ), E<4, 24,

DIMENSION

03(4,24,29),EX7SS<4,24,29).EXTAlN 4 24 2

L

SAK

k

24 .

29). £LAMG<24, 29>, SÖFYI (24, 29), S,GFV£*24, 29;

DIMENSION PBOL(24,29), XADD(4>,R <25),MO<10)

DIMENSION D1 '

)

4, 24, 29) .

£1 <4, 24, 29;

DIMENSION BE C 4, 29, 24, 24), DEC4, 29, 24, 2 4 0 ETA (4, 29, 24- 2-"--

COMMON/ AM. I i /Q

i (4, 24. 29 )

COMMON.' AK 14/S ( 4, 24, 29)

C0MM0N/KAYN3/SGFY3< 24, 29)

C0MM0N/SINIR/IS1 (70S 182(70), JSI <

70 >, -JS2 (70)

COMMON/SACKY/Sl<4, 24, 29)

COMMON/701/TO°1(24, 29)

COMMON/SSAC /BIGS < 4, 4, 70)

COMMON/SFIS/X(4), XMU(4,70),SGFI•4- 70)

COMMON/AL1/KMAX,

IMAX,

JMAX, III,JJJ, IB

COMMON/AMXMM/AMXG \

7 ,

AIİNÖ ( 7 >

COMMON/PAYYY/ P A W

COMM

ö

W

/

£

p

îj

I /

E S 1 .

•

ICAP, iQEQ, I

AD, IGUC, IBAK. ICEY, KOMSA

C

QMMON/DISIT/I

t t

ip

COMMON,EPS/EPS2, EPS3

C

OMMÜN/EFF/EFFK2

COMMON, HAC 114/ V < 24, 29 )

C

O

M

M

n

N

/

p

O

U

C

U

/

P,

2

KARE, HYUK, IBIS

C

0I1ML- ;

•

AL2/DEER I (24 ) DELZ

v

.

<

(

29 »

COMMON/SAB/SIGAI4, 70)

COMMON/DÎFK/OF?(4, 70>

EG-/1 LA:. Ef-JCC. (DE. 3N1 >, CETA, SN2), (BE, RR)

E.QU I VAL EN C E (A , G.İ

CA

l

-

.

.

OKU

r Iss^MAV

NI" 1 n

A

V

NaW / M A X nr |>U iv'CC* ryr, r;fI"

1C, 03; #

( D *

PS), CE/ S)

*

'

.

?

'A - 1 XK 1

■

f

3 w

— i

:;94 1 — i.

Ni

v95 J~1 ,

N 1

N, 1

~

J) —0, ’

-

■

.

w I •

w

-

! j )

- .

M ,

1 .

-J)

srfi

> /

3 1 ;

J ’

Lr.j

3. I

j

*

•

*

*

0

,1

r

Î

-

■

1

s

,

v/

ij 0 9 5 0 9 4 093

^00

C ÖO

T

; n-j e İ .fO.JE «23-m Cr

a o o PI-3, 3 4 i592 E F F K

1

*J .

0

EFFK2-1.

DO 484 K=l.KMAX 00 405 !-•' , »MAX DO 486 J~J, .»MAX v t(H i - u : -

1

.o VI U K , L J ■■ o F 3 1 K» I. J ) -Ö.

0

SÎK, I, J > =

1

. 0

486 CONTINUE

485 CONTINUE

484 CONTINUE

255 KAT«0

KK-0

IZZ*i

EPS1-0. 01

IF < I

AD. EQ. i Î GOTO 282

REMUVUL TESİR KESİTLERİNİ HESAPLAR

M*1

DC 735 K~1,KMAX

1*1=41+1

IF(M—KMAXJ 161

i

16 i-

16

161 DO 19 NK=1> IS

TOP—0 0

DO 15 N=M,KMAX

TOP-TOP+SIGS (

Ki N, N K )

15 CONTINUE

SIGAIK, NK ) ~ rOP+SIGA {K ,

NK / +DFZ i K, NK 3 «-BKARE

19 CONI IHUE

GOTO 735

16 DO 505 NK— 1iIB

S

î

0

A < K,

N K ) -S

I G'A < K -

NK >

•*•£<=■

Z(L NK )

*B

KARE

505 CONTINUE

735 CONTINUE

DO 7 K— I#KMAX

DO 570 NK-1>

IE

TOZ-DFZ(K)MK«

NS

İ

=

î

S 1 (NK?

NS2-I82(N K )

KSl=USi(N K )

KS2«J82iNK>

DO 580 I ==NS İ ,

NS2

DO 590 J—KS1/KS2

D •

K ,

I. J ) ~TuZ

590 CONTINUE

580 CONTINUE

570 CONTINUE

7

CONTINUE

■24-DO 35 R

=

î,KHAX

DO 45 1=1,IMAX

DO 55 J=2,UMAX

Dİ (Hr l, J )

-2.

»S<K, i, J)*D(K. I -

J-İJ / ( L'E

l

Z

J <

J ) *D t

R, I,

J- 1 ) +DELZU *

'

J- 1 )

*

1D (R

>

I,

U )

)

55 CONTINUE

DO 65 J=1,UJJ

E (R ,

I, J) = 2. *D(K, I-

I, J+ 1 )

/ i DELZü (J+ İ ) *D (K, I- U> +Dt'L?..'=

1,1, J+1 > )

65 CONTINUE

45 CONTINUE

DO 75 J=l,UMAX

DO S5 1=1,III

C(K. 7. UJ«<3. *D<K, I. J)*D(K, 1

+

1, J) )/<DELRI< I

I I, J)+DELRI (

ID'4 I,J>)

85 CONTINUE

DO 95 1=2,IMAX

XV, R/ QEChrJTRILEHI ICIM FARK DENR

LEHLER i

U 1N K

a t s a

t ILAR INI HESAPLAR

e<K. I, 0>=2. *£•<*- 1-

1-1, j:/(DELRI (

Î-İ

I, J)+DELRI Î >*

1DCR,I-İ,J ))

95 CONTINUE

75 CONTINUE

35 CONTINUE

DO 70 K"1,KMAX

DO 30 -J-l >

UMAX

EVTS5<K, 1, UJ=a 0*0vR, 3,0 >

EXTSStK. 2- j:-=2. 0*0 ÎK, IMAX, J>

CO*, IMAX, J)*-D<K. IMAX J ’

/ >

'

EXTSS (K, ?, O i -:-DE.LR I < I

MAX >

/2. >

IF I I

CAP. EG. 1 :

■

GOTO 50

B(R, İ, ■!! --D ■

'

V\- l. > / (L

X

ISO (K l,

U -

-‘

-DEL R I ■

1 ;

•

/

2. >

<SOTO 30

50 B(K, 1. U)=0. 0

30 CONTINUE

DO 60 I=l,IMAX

EXTAU :

k

.

I ■

1 •

=2 .»D.

R ;

•

1 >

E x t AS.- ( R , I ? • = 2. ,3 . i> •• R . I , UMAX )

E :

X,,

I.

<

JhA

X •

=

-

•

D i

X,

1, UMA

X ;

/ ( EX

TAÜ (Ş

;c T D ' £3 1

Q:-.rr 88

>

+DELZ.J (

UMAX ) /2

Di .

*

i —

l

'

r

■

', :,

•

- x 7

a

<

j

,, : i

GOTO oO

)

i /;. >

88

01 '

h.

I ■

1 •

=0. 0

60

C

ON 7

;

T’O

Cf<*v r; uuT

'

ur'

1

GF'C* GO 3

,

;

GOTO 1 *>5

f - 9 1 ? 0 T - - 1 rrlA X : in _DO-- J~1 r J M X v e 1• %J / -•UELRX e r •• 1 2 0 COGT O T DO 1 . R --: , *MAX 1:0 1 4 0 i - 1 I MAX DO 1 5 0 UMa

!-■25

o

o

cj

DICK- I, o > -D 1 < K, ı, J ) -*DELR I C 1 )

EiK, I»

U > =E( K, l, J ■

■

*DELR I < T )

C(K, I, -J ) -C (Kı I, J )

»DEL2

J < J >

B < K, X, J)=B(K, I, J > *T>£LZ

J ^ •)

D (K,

I, J)=D1CK 1 -

J)

150 CONTINUE

140 CONTINUE

130 CONTINUE

00TO 220

155 R C1)—0 0

DO 3 1

=

1,IMAX

R < I

+

İ ) =R < î > +-DELR I t

I >

3 CONTINUE

DO lfcO 1 =

1, I

MAX

DO 170 J=l, UMAX

V< I, J ) =PI-ss-CRf I-*-l )**2-R( I >*«-2;*DEL2J( J)

170 CONTINUE

160 CONTINUE

DO 180 K=1,

KM

AX

DO 190 1

=

1, IMAX

DO 200 J=i, UMAX

Dİ (K, I, J)=Dİ <K, I.. U)*PI*(R< 1

+

1 > **2~R ‘

I s **-2 )

E<K, I,J)=ECK, I, J>*PI*(R<1

+

1 >**2-R(I>**2>

C (K> I,J)=C<K, I, J>*2. *PI*DELZJ<J)*R(1*1>

B (K, I, U)=B<K, I, J >-»2 #-FI

«-DELZ

J< J ) *R C I )

D<K, I, J >=D1 (K, I, J)

200 CONTINUE

190 CONTINUE

180 CONTINUE

220 DO 515 K » 1,KMAX

DO 525 NK=1,

IB

NS

1

=

IS 1 CNK)

NS2=IS2<NK>

KS

1

=JSi<NK)

K8 2

«JS2

(NK)

DO 535 I=N5i, NS2

DO 100 J=KS1, KS2

A (K, Î, U>*E<K, I, J>+C CR, I, Jt+Dl <k, I, J)+BCK, l, J/^-SIGACK, N K ) *V < I,

U )

100 CONTINUE

535 CONTINUE

525 CONTINUE

515 CONTINUE

m a t r i s l e r i k u r a r

B-TERS,

w m a t r i s l e r i n i h e s a p l a r

CALL YURUCA, E, C, D, E, BE, DE, ETA, Kl, NX, NJ)

CALL KATSA < K I ,

NI.- rJJ, BE, ETA. DE, SN2, S3, RR, SN1 )

282 CONTINUE

DO 8001 K=i,KI

DO 8001 1=1,NI

DO 8001 J»1,NJ

ACK, I. J )^0

B(K, I, J

>=0

•26

C < K» I -

J)«0

E<K, I- J)~0

D(K- I, J>=0

8001 CONTINUE

DO 745 1

=

1- IMAX

DO 755 J=l»UMAX

DO 10 K=1»KMAX

G1 <K- I- J ) =1.

Q3<K, I- J)=l.

S<K, I, J) =

l. O

10 CONTINUE

SGFYKI, J)~0.

SGFY2< I -

J)=0. O

SGFY3(I -

J)=0.O

755 CONTINUE

745 CONTINUE

DO 115 K=l,7

AMNQ(K)=1.

115 AMXQ(K)=1.

ITTIR=0

IF< IAD. EG. 1 > GOTO 401

CALL FISYO

CALL GARTl

CALL PAY

PAYDA»PAYY

GOTO 53

401 CALL FISYAD

53 ITTIR=ITTIR+1

DO 450 K=l-KMAX

DO 451 1

=

1- IMAX

DO 452 J=l- UMAX

Q3<K- I, U)=G1 <K- I, J>

452 CONTINUE

451 CONTINUE

450 CONTINUE

IF( İTTİR. GT. 20) GOTO 999

IF( IAD. EG. 1) GOTO 89

GOTO 681

89 DO 917 1

=

1, IMAX

DO 918 U=1 - UMAX

S A K (I,J)=SGFY3<I, J)

918 CONTINUE

917 CONTINUE

681 CONTINUE

CALL CÜZ2 (KI- NI, NJ, Yİ, SN1, SN2- RR- FS, SS- Yİ 1

>

IF(EPS1.

LE. 0. 00004) GOTO 33

EPS

1

=EPS1

*0. 1

33 IF( IAD. NE. 1) GOTO 921

DO 922 1

=1- IMAX

DO 923 J=1 -

UMAX

SGFY3(I-U)=SAK(I

-

J)

923 CONTINUE

922 CONTINUE

-

27

“

a n a

921 DO 700 1

=

1. IMAX

DO 800 J=l, UMAX

SGFY1(1/0)»SGFY2<I,J)

SGFY2f!.J >=SGFY3Ü . Ü )

800 CONTINUE

700 CONTINUE

IF ( I

AD, EQ. 1 ) GOTO 407

CALL FISYO

CALL PAY

EFFK1=EFFK2

EFFK2=PAYY/PAYDA

WRITE(6,13) EFFK2

DO 58 1=1,IMAX

DO 68 U=l,UMAX

SGFY3 ( I, J) =SGFY3 < I, J) /EcrFK2

68 CONTINUE

58 CONTINUE

GOTO 935

407 CALL FISYAD

935 DO 225 K=l, 6

AMNG(K)=AMNQ(K+1)

225 AMXQ<K )=AMXQ<K+1)

C

C

FISYON KAYNAK TERİMLERİNİN ORANLARININ MAX VE MIN LARÎNI BULUR

C

AMX=C\ O

AMN=0. O

KAZ

= 1

DO İlli 1

=

1, IMAX

DO 216 -J—

1, UMA

X

IF 1SGFY3( I/ J). EQ. O. ) GOTO 216

IF< SGFY2< I, J>.

EG. O. ) GOTO 216

IF(KAZ. EG. 1) GOTO 421

ELAMQ(I•

U > =SGFY3(I,

J >/SGFY2<I,J)

GOTO 5522

421 KAZ=2

ELAMQ<I,J)=SGFY3(1, J ' /SÖFY2(I,

J )

AMX=ELAMG<I, U)

AMN—ELAMG(I, J)

GOTO 216

5522 IF<AMX-ELAMG(I ■

J ) ) 1725, 48, 48

1725 AMX=ELAMG<I, U>

48

IF(AMN~ELAMQ. \ ■

J> ) 216, 2le,, 73

73 AMN*£LAMG ( I,

)

216 CONTINUE

İlil CONTINUE

AMXQ(7>=.-AMX

AMNQ ( 7 > --AMN

IF <ITJ

î

R—3 ) î i 1,

1 t 1, İ 22

111 XF(IAD- E9. İ > GOTO 53

•28-o o o

CALL QARTl

CALL PAY

PAYDA=PAYY

GOTO 53

122 IF a AD. EQ 1) GOTO 577

X

Y-ABS(EFFK2-EFFK1)

577 X

YY'-AMX

Q (7' —AMNQ (7)

IF (XV GT. EPS2 GOTO 458

IF;XYY GT EPS2) GOTO 458

459 DO 2001 K=l,KMAX

DO 2002 1

= 1 i

IMAX

DO 2003 \J—

i ,

JMAX

FARK38

Afi

S (Q3 (Ki I, J)-Q1 (K, I, J> )

IF<FARK GT. EPS3) GOTO 458

2003 CONTINUE

2002 CONTINUE

2001 CONTINUE

GOTO 999

458 IF<İTTİR. LT. 7) GOTO İli

DIS ITERASYONDA CHPCEF HIZLANDIRMASINI YAPAR

IF (KK—2 > 103,24,32

103 IF (KAT. EG. 1) GOTO 24

KKK=3

KAT»

i

DELQO« < < AMXG < 4 > -AMNQ( 4) ) / (AMXQ< 7) -AMNQ(7 >)>***1. /3. )

XX=2. «-DELQ0-1.

YY=ÂLOG(XX+SQRT(XX**2— İ. >)«KKK

YY*(EXP(YY> +EXP(-YY))/2

ERUS=1 /YY

ALF=1.

BETA=2. / f 2. — < 1. /DELQO) /

GOTO 523

32 ER= < AMXQ<7)-AMNQ(7))/(AMXQ < 4>-AMNQ14))

ÎFCER-ERUS) 623,623, 723

623 KK=0

GOTO 24

723 AK*ER/ERUS

ASS=1./KK

ASK-ALGG< AK+SQRT < AK**2-1. ) -*ASS

ASK=2. *D£LQO/(((EXP<ASKJ+EXP<-ASK)>/2 )+i. )

DELGO*ASK

b e t a

*2. / 1 2.

1- /DELQO ) )

XX=2. «

DELQO-1

YY«4L0G<* X+SGPT(X X*#2-1 ))*KK

vy= ( exp (YY) +EXP (-YY > )

/2.

ERUS=1. /YY

KK=0

24 DEK.= 1. f (

BETA-1. >

DD*AL0G(DEK+SQRT(DEK**2-1 . ) )*IZZ

DO— ( EXP i

DÜ •

+EXP (-ÖD ) >

/2

rzz=jzz+i

DEE=ALQG (DEK+SÖRT (D‘

\.

>

i

* T 2 3

DEE= (EXP (DEE ) +E’

*T

i

-£>EE > > /2.

DEK=DEK#2.

ALF=DEK

*• (DD

/DEE )

523 DO r.Oi 1 7*1, : MAX

DO 201İ Js-l.JKAX

S4FY3 < I,

J > =SGF\ t

;

1, j M

a

!

)>

(

Ü0rv2 (I,

J )

- ;>Gr '/1 < T <

J ) +

ÎSETA* < SGFY3 (I, J>

İ

SGF

V

2 i

20

a

1 CONTINUE

İ01i CONTINUE

C

c

c

KK=KK+1

IF ( I

AD. ME. 1 > GOTO ill

DO 805 K=i,KMAX

DO 806 NK=1>IB

Mi-131(NK)

N2=IS2 iNH)

K1-JS1(N K )

K2-JS2(N K

)

DO 807 I=N1.N2

DO 808 J»K1,K2

S(K, I, J)-SGFY3t I, J>«XNU(K, N K >*SGFI(k, NK) /EFFK2

808 CONTINUE

807 CONTINUE

806 CONTINUE

805 CONTINUE

GOTO 111

999 WRITE<6,13) EFFK2

DO 2010 1

=

1 ,

IMAX

MQ<I)=I

2010 CONTINUE

DO 1 K»l,KMAX

IF( IAD. NE. 1 ) GllT0 ^

at

WRITE(6,109) K

WRITE(6.1100)

GOTO

W 8

777 WRITE(6■888) K

WRITE(6,1100)

108 N=1

M=lO

2060 WR I TE < 6, 2030) < MO < I ), I =N, M >

DO 2040 LI

,UMAX

J—JMAX—Ll-i-l

WR

1

T

E < 6, 1İ3; J, (O) iW, 1. J), I--N. M>

2040 CQNT1NUE

write

:(6.

i

ico)

1F(M.EG IMAX) 30 VO 1

n

=

m

+1

M«M+10

Ip <M.

GT

IMAX) M~IMAX

GO TO 2060

1

CONTINUE

WRITE (6. 14; iOrjR

IF 4

NRfi 30. 2> GOTO 4?8

IFi£AO

cu

-

•

c

C

KAFESLERDEKİ GUC VE KAYN

a a

:C

a

C:^.İLİL

j h e s a p l a r

c

T

T~0.

o

I)G &G0 3

IB

Nİ-IS1( N K >

N2=IS2iNK>

Kt«J3 l *

NK. >

K2=US2<N K >

DO İl I-~N

1, M2

DO 21 -J*Kİ. K2

T»0. 0

DO 31 K=l,KMAX

T*»T+SGFI (K

cfc, l.

j>

31

CONTINUE

SGFY3 *

>

I J ) «T

TT*TT+T*V ( I,

J ) *2 *HYUK/PI

21

CONTINUE

11

CONTINUE

6005 CONTINUE

E K A T C O O *i. 602IE*-13

t t=t t *e k a t

AKAT«P/TT

IF < ICUC -

NET t / OOTQ 6065

T0P0U--0. 0

DO 4 İ 1

= 1- IMAX

DO 51 J~1,

UMAX

PQOL(I,u)=AKAT«EKAT*SGPY3CI, J}*V<I, J-*2. *HYUK/PI

TOPGU=TOPOU+PBOL<I, J)

51

CONTINUE

41

CONTINUE

6065 1F(IBIS EG. 0/ GO İL YO6

DO 210 1 =

1, 1MAX

DO 795 J~l*UMAX

SG

f V3 *

:

1, -J s ^ÇGF /3 >

I *

u ■

;^KAT

DO 230 i

-

'

-

- 1. JO-'ft*

01 • 'A ■ i •a 1 ~0) I. V»; > -VaAT

230 CON'- INUE

795 CONTINUE

210 CONTINUE

DO 340 V.~i

j

KM

AX

U R i H I u T ,.CC > K

WRI Tt î

ft ,

5 J O O '

N=1

«*•10

207G WR £ : r ( 6 •

2030 > \ MC Cl.», 1 »N, ii 1

DO 2C00 'U = : -

-/MAX

U=UM,*-.

X *t Ifl

w r i T k. ■,, : t o > . s - <* i k . i j • : «n ■ ■ n

2080 COwr ■

N»jr

WRITE 16. 1130)

I F '3 EL I M A X '

GO -• 340

“31-n

n

n

N-M+l

Îİ=M+10

IF(M GT IMAX) M=IHAX

GO TO 2070

240 CGNTINUE

796 IF<IGUC. NE. 1> GO TO 797

WRITE(6ı 61)

W R I TE (6» İİÖÖ) N

=1

N=İO

2095 WRITE(o, 2030) ihQ(î), Î=N, M)

DO 2090 LÎ=İ.JMAX

J=JHAX~LI+1

WRITE<6, 118) J, <PBOL( I, J), I=N, M)

2090 CONTINUE

WRITE*- 6ı 1100)

IF(M EG. IMAX > GO TO 6075

N=M-1

M=H+1Q

IF»

M, OT. IMAX 5

H-IMAX

GO TO 2095

6075 CONTINUE

MRITEÎfc, 6085)

WRITER i>, 1100) N

=1

M

»10

3020 WRITE ?

ö,2030) (KO (I)< I-N,M>

DO 3010 LI

=

1,UMAX

J=UMAX-L1+1

WRITE<6, 118) -J, (SGFY3( I. J), I*N, M)

3010 CONTINUE

WRITE(6;1100)

IF (M. EG. IMAX) GO TO 121

N*M+1

M-M-s-10

IFCM- GT. IMAX) M=IMAX

GO TO 3020

121 CONTINUE

WRITE(6,18) TOPGU

797 CONTINUE

1GUC~u

IS i'3~0

';.a d=i a d+'j

IFC fAD GE. 2) GOTO 498

GOTO 255

498 CONTINUE

330 FOR

MAT(2X< 30 2X 1 OF12. 5)

300 FORMA

I !

OX <

Î2-

NCI GRUP NORMALIZE AKI ')

6085 FORMXr •

W KAFES HACİMLERİNDEKİ KAYNAK DACILIMI '

61 FORMAT.. ıx, '««FES HACİMLERİNDEKİ GUC DAHİLİMİ '

*

18 F O R M A T <5/, 'TOPLAM REAKTÖR GÜCÜ” ' - E '.4 7)

109 FORM A T < 5X T2- NC I GRUP ADuülNT AK: DEĞERLERİ') 888 FORMAT <jX, 12 '.NC. GURUP ESAS AKI ECO ERLERİ ‘ )

118 FORMAT (21.. |3, 2X, İ0E1.2. 5:

13 FORMaÎ U T 'K EFFEKİ IF- Eİ4 7) 2030 FORMAT*. ;2 4> 9C4X. 12, 6X) >

İ 4 FORMAT ( 1 a , 'DIP 1 TER AS YÜN SAY 1 T f ~ *', i'2 ) 110 FORMAT*'//) 1100 FORMAT </> STOP END C SUBROUTINE OKU

c

C GRIS OATALAR INI OKUR VE YAZAR C

DIMENSION MM C 24, 29), DF ( 4. 11 ), SA (4. 11), SF(4, 11 ), SS ( 4 , 4, li>, XN < 4, 11) COMMON, SINIR/rSl (70), 132(70), J S D 7 0 ) , JS2i 70)

COMMON/SSAC/S î GS (4, 4, 70)

COMMON/SFIS/X < 4), X N U (4,70), S G F I (4, 70) COMMON/AL2/DELR1(24), DEL.Z J '29)

COM M O N / D I FK/DF7(4, 70) C O MMON/3AB/5IGA<4, 70?

COMMOn/AL.1/ KMAX, IMAX, UMAX, Ill UJu. ID

COMMON/EPSI/EPS! , ICaP, ICED. IAD, IGUC. IBAK, ICEY, KÛMSA C0MM0N/EPS/EPS2, EPS3

COMMON/P5JCU/ P-BkARE.NYUK,IBIS D i MENS ION IMAT i^ 0 >, KK < 70 >, N M (70) P I-3. 141592

RE A D * 5 83) EP32, EP33

R E A D <5-13) IB, ICAP, ICED, IAD, IGUC, IBAK, ICEY,KMAX, IMAX, UMAX, ROMSA, 1 IBIS

WRITE!*, 13 > IB, I CAP. IGEO, I AD, IGUC, IBAK, ICEY, KM A X , IMAX, UMAX. KQMSA 1IEIS

READ*. 5. 23) < 1ST (E , T%Oe. ‘.k :* , J3JL *K ).JSI? (K ). V ~İ , I 8 •

-m : t v *:b. 24 ) * K , i3 1 (K l32 * K >, JS1 (K ) ,JQ2 (K ), K*= 1. İB) 24 FORMAT'X X3 I"415, 2X. 4 _Î5) R E A D (5 ■25; ( (KK'K j.*I MAT i;kj■ >, K=- 1, 1B ) 25 FORMAT*. 1814> W R 1 T E (ib, 26 :• < ( k k (K }, I M A :" ( K > ) ; V 1, IB) «*0Di _{FORMAT -• sd A f 1814:*}

READ f 5, 33) * OdLR 1 (I ) .. 11- İ, IMAX) RErtD *. 5, 33 ) (DELZ j ('ij f / = 1, •A MAX > DO 200 k-1 . KM AX DO 310 IM«1 , KM AX DO 320 Ntr‘J~ 1.K0M3 A SS i K N, tm >=0. 0 20 CQNTIni’E 310 CONTINUE 300 CONTINUE READ ( 3, 23 ? M

~0

( X ;K ; K~l, KM AX )

M-n+ı DC 20 N N * A, K0M84

SEAIMÖ. 03 ) XN <

.

K» !

v

;N> DF(K, NN >, SA •

'

'A ı^N) >

SF-:K, NN ) >

(SS(K> N, NN)> N=M< KMAX

1 ) 20 CONTINUE i:-ü so :t NN- 1 'iAT < NK ■ XNU (¥•, NK)-=XN' O, NN) D" Z N K ) ~DF *. v . NU) SIG A (K NK '* - S A (K .■ N N ) SOF î (. K • MX ' ~SP (K NN ? DO 40 W=M KMAX S î ÖS (y.t N ( NK ) =--Sö <K . N, NN ) 40 CONTINUE 30 CONTINUE 10 CONTINUE ÎFC ISUC. NE. 1 > 03^0 11 R E A D (5. 32) P

11 IF! IEAK. NE. 1 > 0370 12 R E A D (5, 53) HYUrt

BKARE« (Pi/ HYUK * + *2. GOTO 14

12

B K A R E

“ 0

0

HYUK-P I /2. 14 WR I T£ 6 • 15 • KrlAX .13, KÖMSA W R I T E (6-145) WRITEC6, 155) P WRITEtto,I45)

Ir(I GEO EC- i > GOTO 201 W R I T E (6,335)

WRITE (6, 145)

WRITE < 6 1 6 5 )

l

rtAX, JMAX

W R I T E (6,145)

W R I T E (3,175)

WRITEI6, 65) (DE-..P I v I , I - 1 . i MAX ) W R t ”E ( 6 . 145) WRITEifc i65> WRi T£:*. o 5 ) (P E L 2 U u 2 . •)~] > U M A X ) GOTO -202 201 WRITE-t, 2^5) WRITE!6 - 145)

WR 17E . 6• 195) INAX *JMAX wRI're (

6

- 145)

WRITE(A. SC5>

WRITE ( h, 65 :■ i DEI 7 I < I : I-i . 1 f1AX > WRITE (6. J 45)

W R I T E <£.215)

WRITE' 6 • t.Z. ( DEL. Z-J ( J ] U= 1, UMAX > WR Î T£ s' 6. 1 2-5)

WRIT£(6.235) 202 DO 70 K - l . K H A X

WRITE\t. 145 >

WRIT£ <

6' 105/ K

WRI 7FC6, 245;

L'O SO NN=

11

KOMSA

WR i

re

'

to,

1

] 5 > NN, XN < K, NN >,

(K, NN 5. SACK, NN),

SF < K ,

NN ) :

35 <

K, N NN ) ,

N

1-1.KMAX)

SO CONTINUE /O CONTINUE wft ITE (6, 145)

WRITE <6.- £55)

WRITE(6,145)

DO 120 NK=1, IB

OQ 110 J=l, JMAX

N1=I31 INK)

N2— IS2<NK)

K 1=031< N K )

K2=U82<NK>

DO 130 1

=

1, IMAX

14(1 LT. N 1 ) GOTO 130

IFÜ. GT. N2) GOTO 130

IF( J LT. K 1 ) GOTO 130

IF< J. GT. K2) GOTO 130

M M ( I,

J > =

IMAT < NK)

130 CONTINUE

110 CONTINUE

120 CONTINUE

L3=JMAX+1

DO 150 U=1iJMAX

KN=JMAX+1~J

L3=L3-1 W R I T E (6, İ35JKN, < MM ( I, L3>, 1 = 1, I MAX)

150 CONTINUE

WRITE <6, 145)

DO 151 î

= l, IMAX

N M ( I) - I

151

CONTINUE

WRITE (6, 121 > (NM( I ), 1 =

1, I

MAX)

121

FORMAT (25X,5012)

III*IMAX-1

JJJ=JMAX-1

WRITE(6-145)

WRITE(6,98) E°S2, EPS3

98 FORMAT ( 5X,

*

K-FF VE FIS. KAY. HAS= ", Flu 7. 5X, AKI HAS= ', F10. 7)

13 FORMAT(1213)

23 FORMAT(413)

33 FORMAT (8F10. 5)

53 FORMAT(El4. 7>

S3 «FORMAT <SF 10 7)

15 FORMAT( 5X, 'GRUP SAY 131=

12- 5X. 'BÖLGE SA\ 1SX - •

.

12, 5X, 'KOMPOZİSYON

1SAYISI=',12)

65 FORMAT(3F10. 5)

■35-o

o

SGM ABS

SGM F

i 0?.>

fcîrj

-

a

T CSX, 12/

İMCİ GRUP ICIN

NU

C>^ L£r

i -.i'

SGM SCI

SGM SC2

SDM SCCi

SGM S04 ')

3 e" FORMAT( 5X» 12, '

NCI KÛNF

L (3FU>. ?) *

1 LC FORMAT (21 X, 12, -2X 5 0 1 2 ’

1/5 ^DRM

a

TC/ >

i

.

S

5

FORMAT I5X,

'REAKTÖR GÜCÜ---', El4. 7. 'WATT TERMAL '

>

l

'T,

FORMAT* 5>.,

"X YONUNDEK 1 KAFES ARALIKLARI ' >

185

F0RMATC5X,

'V YONUNDEKI KAFES ARALIKLARI'

;

i *-6

FORMAT <5X,

'X vONUNDEK l KAFES ARALIKLARI SAYISI* , 12, 3X, 'V YÜNÜNDEKİ

i KAFES ARALIKLARI SA

y î

SI-L 13'

İ

95 FORMAT*. 5X, "R YÜNÜNDEKİ KAFES AR

AL

I

K

l

.

AR T SAYISI*', 12. 5X, 'I Y

ÖNÜNDEKİ

1 KAFES ARADIKLARI SAYISI* ", 12)

205 FORMAT <5X2 "R YONUNDEK I KAFES ARALIKLARI ' >

219 FORMAT <5X, 'Z YONUNDEKI KAFES ARALIKLARI')

235 FORMAT<3CX, 'TESİR KESİTLERİ 'ı

245 FORMAT s

26

X, '---- -—

2X

~--- ',2X, '— --- -

',2X,

'---12X,

2X, '--- ,

4X,

--- 'L 3X>

---')

255 FORMAT(OCX, 'KOR KQNFIGIRASYONU‘

)

335 FORMAT i33X, 'X-Y GEOMETRİSİ )

345 FORMAT(33X, 'R~Z GEOMETRİSİ)

RETURN

END

C

SUBROUTINE FISYO

rİSYON KAYNAK TERİMİNİ HESAPLAR

COMMON/HACIM/ VC24,29)

COMMON/ALİ/ KMAX,IMAX,JMAX,III,JÜJ,IE

C0MMQN/KAYN3/3

ö

FY3<24, 29)

COMMON/SINIR/ ISîL 70 >» IS2<7ö>, JBK70), JS2C70)

COMMON/AKI l/G1 <

4, 2*. 29)

CQMMCN/SFIS/X < 4 >, XNU<4, 70).SGFI(4,70)

00 S NK=1, IB

NS1 *

î

SI<NK)

NS2*IS2<NK>

KS1*US1< N K )

KS2*US2<NK>

ÛO İl I*NS1 ,

NS2

.00 2İ J=KS1, KS2

TQP—Q.

00 13 K*l,KMAX

T

OP«TOP +-SGFI i K, NK >*XNU(K, m >*G1 <K, i, -J)*0( I, ))

13 CONTINUE

SGFf3(i. j) "TOP

2 i

CONTINUE

1

CONTINUE

8 CONTINUE

RETURN

END

36

a

a

a

a

a

a

a

n

o

a

SUBROUTINE PAY

H-EFF DEKİ INTEGRA

l

LERi HESAPLAR

COMMON/ALİ / KMAX, IMAX, UMAX. 1

U -

J.Jw-

I B

COMMON/HACIM/ V<24,29)

C 0 M M 0 N / K A Y N 3 / S G Fy3(2*, 29)

COMMON/TO!/TOPI(24, 29)

COMMON/PAYYY/ PAYY

T«0 0

DO 1 1 = 1, IMAX

DO İ1 U*l, UMAX

T—T+TOP1 < I, U>*SGFY3(i •

U >* V iî, U î

11 CONTINUE

I

CONTINUE

PAYY*T

RETURN

END

SUBROUTINE QARTI

K-EFF HESABINDAKİ ASIRLIK FONKSİYONUNU HESAPLAR

COMMON/ALİ/ KMAX, IMAX, UMAX, III, JUU, IB

COMMON/AKH/Q

1(4, 24, 29)

COMMON/TOl/TOPl<24, 29)

CQMMON/EFF/EFFK2

DO 1 1*1, IMAX

DO 11 U*l, UMAX

T O P U I, U)=0. 0

DO 21 K»l. KMAX

TOP 1 < I, U>»TOPKI, U)+GKK, I, U)/EFFK2

21 CONTINUE

II CONTINUE

1

CONTINUE

RETURN

END

SUBROUTINE FISYAD

ADUOINT AKI HESABINDAKİ FISYON KAYNAĞINI HESAPLAR

COMMON/SINIR/IS1 (70), IS2C7G), US1 (70), JS2C 70)

COMMON/AK 11/Q1 <4, 24, 29)

COMMON/AL1/KMAX, IMAX,UMAX, III, JUU, ÎB

C0MM0N/KAYN3/SÖFV3 <24, 29)

COMMON/SFIS/X<4), XNUC4. 70), SGFÎ

i

4, 70)

COMMON/AK14/S < 4, 24, 29)

COMMON/DISIT/ITTIR

COMMON/EFF/EFFK2

DO S NK=1, IB

NS1*IS 1(NK)

NS2=IS2<NK)

KS1*US1<NK)

KS2=US2<NK)

-3T

DO 11 I=NS1,NS2

DO 21 U=KS1 , KS2

T0P=0.0

DO 15 N=l,KMAX

TQP=TOP+X(N)*QlCN, I, J)

15 CONTINUE

SGFV3C1 , J)=TQP

IP(İTTİR.GT. 7) GOTO 21

DO 31 K=l,KMAX

SCK, I,U)=TOP*XNUCK, NK)*SGFI<K, NKJ/EFFK2

31 CONTINUE

21 CONTINUE

11 CONTINUE

8 CONTINUE

RETURN

END

C

SUBROUTINE YURUCA, B. C. D, E, BE. DE. ETA, KI, NI, NU)

C

DIMENSION AC4, 24, 29), B<4, 24, 29), C(4, 24, 29), D<4, 24, 29), E(4, 24, 29)

DIMENSION BE<4, 29, 24, 24), DE<4, 29, 24, 24), ETA(4, 29, 24, 24)

DO 410 K*l, KI

DO 430 J*l, NU

1*1

N=J

IF<

J. EQ. 1) GOTO 440

IF (J. EQ. N U )GOTO 450

IFCI. EQ. 1) GOTO 460

480 IF(I.

EQ. NI) GOTO 470

DECK, N, M+l, L)*=“D<K, I, J)

BECK, N, M, L)*-BCK, I, J)

BECK, N, M+l, L>=ACK, I, J)

BECK, N, M+2. L)=-C(K, I, U>

ETACK, N, M+l.L)=-E<K, I. J)

1 * 1

+

1

L=L+1

M=M+1

GOTO 480

460 M=1

L=1

DECK, N, M, L)=-D(K, I, J)

BECK, N, !İ, L )53A (K ,

I, J)

BECK, N. M+l, L)=~CCK, I, J)

ETACK. N, M, L)*-ECK, I, J)

1

=

1

+

1

L=L+1

GOTO 480

470 DECK, N, M+l, L)=“D(K, I, J)

BECK, N, M, L)=-BCK, I, J)

BECK, N, M+l, L)=A(K, I, J)

ETACK, N, M+l, L)=-E(K, I, J)

3 8

-Q

O

O

GOTO 430

440

IFC

I. EG i) GOTO 49G

5C0 IF' I EC. N D GOTO 510

BECK, N, M. L ) =—E (K» i.

BECK,

M, H-H, L >=A '

K ,

I, Jî

BECK, N, M+2, L ) = ~€CK, I, JJ ETACK, N, M + İ , !_)=-EtK. I, J)

1

=

1

+

1

L = L

+1

M = M

+1

GOTO 500

490 M=1

L=1

BECK, N,

M,

L)=ACK, I, J)

BECK, N, M+l, L ) =—C (K, I, J)

ETACK, N, M, L)=-ECK, I, J>

1

=

1

+

1

L = L

+1

GOTO 500

510 BECK, N, M, L>=~E(K, I, J>

BECK, N, H+l, L)»ACK, I, J)

ETACK, N, M+l, L)=~E<K, I, J)

GOTO 430

450 M=1

L=İ

IFC I. EQ. i ) GOTO 520

530 IFC I. EG. NI > GOTO 540

DECK, İM, H+l, L)=~DCK, I, J)

BECK, N, H, L>=~BCK, I, J)

BECK, N, H+l, L)=ACK, I, J)

BECK, N, H+2, L ) =—CCK, I, J)

1

=

1

+

1

L=L+1

H=M+1

GOTO 530

520 DE CK, SM, H, L> =-D CK, I,

J )

BECK, N, H, L)=A(K, I,

J>

BECK, N, H+l, L)=-CCK, î, J)

1

=

1

+

1

L=L+1

GOTO 530

540 DECK, N, M+l, L)=-D<K, I.

J i

BECK, M, M, u J*-*BCK, I, J>

BECK, N, H+l, L f ~A i K ,

I, J)

430 CONTINUE

410 CONTINUE

RETURN

END

SUBROUTINE SACADCK>

ADJOINT AKI HESABINDAKİ SAÇILMA KAYNAĞINI HESAPLAR

-C O M M O N / A L İ /KMAX * IMAX,UMAX, III,JJJ, IB C O M M O N /S S A C / S I S S (4, 4, 70) C O M M O N / A K I 1/01(4, 24, 29) C O M M O N / S I N I R / I S İ (70), 132(70), JSİ < 70>, 032(70) C O M M C N / S A C K V / S İ (4, 24,29) M = K DO 19 N K = 1 , IB NS1=IS1<NK> N S 2 - I S 2 (N K ) K31=JS1CNK) K S2=JS2(NK> DO 70 I = N S 1, NS2 DO SO J=KS1, KS2 TOP=Q. 0 D O 15 N=M, KMAX TOP=TQP+SIGS<K, N, NK)*G1 (N, I, J) 15 C O N T I N U E Sİ (K, I, J>=TOP 80 C O N T I N U E 70 C O N T I N U E 19 C O N T I N U E R E T U R N E N D C

S U B R O U T I N E HIZ(K, NI, NJ, Yİ, Y2, EMX, EMN, OMEG, NTT) C

C O M M O N /EPSI/EPSİ, İCAP, IGEO, IAD, IGUC, IBAK, ICEY, K O M S A D I M E N S I O N Y1 (4, 24, 29), Y2(4, 24, 29) TQP=C. 0 TOG=Q. 0 DO 25 N = 1 , N J DO 30 1=1,NI T0P=T0P+Y2<K, I,N>**2 T0G*T0Q+Y2(K, I, N)*Y1 (K, I, N) 3 0 C O N T I N U E 2 5 C O N T I N U E E L L = T O P / T O G E M X = A B S ( 1. -EMX > E M N = A B S (1. ~EMN> E L L = A B S < 1. -ELL) 0MX=2. /(1. + S Q R T (E M X )) 0MN=2. /< 1. + S G R T (E M N ) > 0ML=2. /( 1. + S Q R T (ELL > ) O X X = A B S (O M X — Q M N ) O Y Y = (2. ™ 0 M L > / 5

IF(OXX. LE. EPS!) GO TO 40 O M E G = O M L G O T O 50 40 NTT=1 50 R E T U R N E N D -40

-c S U B R O U T I N E C Ü Z 2 (K !, M l , N-.;, Y I, SNİ 3N2, RR, FS, SS, V U > C D I M E N S I O N Y22(4,24> 29), Yİ 1(4, 24, 29> D I M E N S I O N SN2<4, 29, 24, 24 > - F S C 4, 24, 29), SS(4, 29, 24, 24), Y2(4, 24, 29), İYİ (4, 24, 29), Fİ (24*;, F2C24), SN)

»

4,

29,

24, 24), ST<24, 29), RT(2 4 , 29), 2RRC4, 29, 24. 24), F(24) C O M M O N / A K I 1 / Q 1 < 4, 24, 29)

C O M M Ü N / E P S I / E P S 1 , İCAP, IOEO, IAD, IGUC, IBAK, I C E Y , K O M S A N X = N J ~ İ D O 10 K = 1 , KI C A L L KAYN<K) C A L L FSFS(K, NI, NJ, RR, FS) Ü M E G = 1 I T E R = 0 N T T = 0 100 C O N T I N U E N=l C A L L FSP <K, N, NI, NJ, N+l, SN2, Yİ, Fİ ) C A L L SQUCK, N, NI, NJ, SS, Fİ, Y2)

C A L L FSP (K, N, NI, NJ, N+İ, SN2, Y U , Fİ ) D O 14 I— 1,NI F ( I ) = F 1 < I )+FS(K, I, N) 14 C O N T I N U E C A L L S Q U (K, N, NI, NJ, SS, F, Y22) D O 16 1 = 1 , NI Y22(K, I, N ) = 0 M E G * ( Y 2 2 ( K , I, N / - Y 1 K K , I, N> ) +Yİ 1 (K, I. N> 16 C O N T I N U E D O İS N = 2 , NX C A L L FSP < K, N, NI, NJ, N+l, SN2, Yl, Fİ ) C A L L F S P (K, N, NI, NJ, N-l, SN1, Y2, F2) D O 3 3 1 = 1 , NI

F 1(I)=F1(1)+F2 <I)

3 3 C O N T I N U E C A L L S Q U (K, N, NI, NJ, SS, Fİ, Y2) C A L L FSP < K, N, NI, NJ, N + l , SN2, Y U , Fİ ) C A L L FSP (K, N, NI, NJ, N-l, SN1, Y22, F2 > DO 2 0 1 = 1 , NI F < I ) =F1 ( I > + F 2 < 1 )+FS(K, I, N) 2 0 C O N T I N U E C A L L S Q U (K, N, NX, NJ, SS, F, Y22) DO 22 1 = 1 , NI

Y22(K, 1, N ) = O M E ö * < Y 2 2 < K , I, N) -Yl 1 (K, I . N) )+Yl U K » I, N)

2 2 C O N T I N U E 18 C O N T I N U E N = N J C A L L FSP (K, N, NI, NJ, N-l, SN1, Y2, F 2 ) C A L L S Q U (K, N, NI, NJ, SS, F2, Y2) C A L L F S P (K, N, NI, NJ, N-l, SN1, Y22, F 2 ) D O 24 1 = 1 , NI F ( I ) = F 2 ( I > +FS(K, I, N)

- 4 1