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SEC!P TRACE: # 1 1 1 » A FUEL CYCLE COMPUTER CODE

FOR FAST REACTOR ANALYSü

íliiite

i i re

Ili

m ii LEGAL NOTIC]

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This document was reproduced on the basis of the best available copy Ι8Γ"

mmáà B i s i s r

EUR 4709 e T R A C E : A F U E L CYCLE COMPUTER CODE FOR FAST REACTOR ANALYSIS by G. GRAZIANI

Commission of the European Communities Joint Nucleax Research Centre Ispra Establishment (Italy) Nuclear Studies Division Luxembourg, August 1971 - 34 pages - B.Fr. 50,—

This report describes a two-dimensional computer program written for the IBM 360/66 which calculates the fuel input requirements and the neutron physics behaviour of the equilibrium fuel cycle of a fast reactor using a partial refuelling scheme.

EUR 4709 e T R A C E : A F U E L CYCLE COMPUTER CODE FOR FAST REACTOR ANALYSIS by G. GRAZIANI

Commission of the European Communities Joint Nuclear Research Centre Ispra Establishment (Italy) Nuclear Studies Division Luxembourg, August 1971 - 34 pages - B.Fr. 50,—

This report describes a two-dimensional computer program written for the IBM 360/65 which calculates the fuel input requirements and the neutron physics behaviour of the equilibrium fuel cycle of a fast reactor using a partial refuelling scheme.

EUR 4709 e T R A C E : A F U E L CYCLE COMPUTER CODE FOR FAST REACTOR ANALYSIS by G. GRAZIANI

Commission of the European Communities Joint Nuclear Research Centre Ispra Establishment (Italy) Nuclear Studies Division Luxembourg, August 1971 - 34 pages - B.Fr. 50,—

This report describes a two-dimensional computer program written for the IBM 360/65 which calculates the fuel input requirements and the neutron physics behaviour of the equilibrium fuel cycle of a fast reactor using a partial refuelling scheme.

I

EUR 4 7 0 9 e

COMMISSION OF THE EUROPEAN COMMUNITIES

T R A C E : A FUEL CYCLE COMPUTER CODE

FOR FAST REACTOR ANALYSIS

by

G. GRAZIANI

1971

Joint Nuclear Research Centre Ispra Establishment - Italy

Nuclear Studies Division

A B S T R A G T

This report describes a two-dimensional computer program written for the IBM 360/65 which calculates the fuel input requirements and the neutron physics behaviour of the equilibrium fuel cycle of a fast reactor using a partial refuelling scheme.

KEYWORDS

FAST REACTORS FUEL CYCLE PROGRAMMING IBM 360 2-DIMENSIONAL CALCULATIONS BURNUP SELF-SHIELDING NEUTRON DIFFUSION EQUATION NEUTRON SPECTRA BUCKLING

INDEX

1. Introduction

2. The burn-up calculation

3. The self-shielding calculation

4. The diffusion calculation method

5. Spectrum calculation and Buckling Vectors

6. The calculation procedure

7. Output description

8. Acknowledgements

9. References

10.How to use

1. INTRODUCTION

In the process of designing a fast reactor, it is convenient, when fractional core loading is considered, to investigate the equilibrium fuel cycle before a large effort is spent in the project. Generally speaking it is possible to reach the equilibrium cycle following the so called "approach to equi­librium" procedure. In this case the calculation starts con--sidering the initial charge to be in the core and calculating the flux distribution and the depletion up to the time when the first reloading occurs. At that time a fraction of the burned fuel is replaced with fresh one. The calculation of the flux distribution and the depletion is repeated till the next refueling time. If this procedure is continued long en--ough, the feed fuel requirements will become stationary and the behaviour of the nuclear parameters will repeat at each cycle. The equilibrium cycle is so reached. This approach has the advantage to give all the informations on the way to the approach to the equilibrium, as well as on the equilibrium cycle itself. However this procedure is quite lenghty and com--puter time consuming. For much of the survey work on fast reactor fuel cycles, data on the approach to equilibrium are not necessary and the calculation of the running in period can be avoided. Actually the selection of a certain number of nuclear parameters from an equilibrium cycle survey is ad­vantageous because the equilibrium conditions of the fuel cycle represent the larger part of the reactor life. The code TRACE is a two dimensional programme (R-Z) written to investigate the parameters of the equilibrium fuel cycle without generating the data for all the approach cycles. The consequent reduction of informations is counter-balanced by a large gain in computer time (in spite of the complexity of the problem). A further source of time-saving is the assump--tion that the spatial dependence of the flux can be well re­presented by one group diffusion calculation: this is accu­rate enough for this kind of fast reactor calculations. Computer times between 2 or 3 minutes can be obtained for each complete calculation on th¡e IBM 360/65 machine.

2. THE BURN-UP CALCULATION

The code allows a depletion model in which the transmutation of a nuclide can happen by neutron capture and radioactive decay. Each nuclide may have up to two capture parents and one decay parent.

Fission yields may be specified for each individual fission

product resulting from a fission of any heavy nuclide.

Provision is made to take into account leakage out of the _1 system of the volatile nuclides by a leakage constant (sec ).

The ..restriction imposed is that no nuclide can be produced

by another nuclide which is in a lower position in the list

of isotopes. This implies that, for example, all fission

products must follow the fissionable isotopes. All changes

in nuclide densities are represented by the system of firèt

order differential equations:

i . i"1

S- = - Α.. Ν1 + Sum Α. . NJ (i=1 , Nue!) (ί) Cit. X_L -î — 1 J

where NUCL is the total number of burnable elements. The coefficients Aij of the system equations form a triangu­lar matrix and represent the transmutation rate (by decay or capture) of nuclide j into nuclide i. The diagonal ele­ments Aii are the total removal rate of the isotope i out of the system. The code assumes that all these reaction rates are time in--dipendent. In fact they are not, because the flux spectrum varies slightly in the reload interval period. However this variation becomes negligible when the number of reloads in­creases, i.e. when the refueling interval becomes shorter. In the fast reactor core, where the conversion ratio is clo--sed to one this flux variation is in any case negligible. In order to reduce the large matrix A, the programme, before solving the burn-up equations, investigates the structure of the matrix, separating the independent burn-up chains, i.e. splitting the matrix A in a certain number of small matrices. One of these will be the fission products chain. On the assum--ptions that the coefficients Aji are constant, the fission product source in the reactor will then be constant, i.e. pro--portional to the average fuel composition of the reactor. This is equivalent to approximate in each region of the reac--tor, the refueling scheme to the continuous reload scheme and therefore to assume that the space averaged concentrations in the zone are equivalent to the time averaged concentrations. This is in most of cases quite satisfactory.

- 7 -

3. THE SELF-SHIELDING CALCULATION

The space and energy distribution of the flux in the fuel cell of a single zone changes during irradiation, thereby affecting the effective cross-sections of the isotopes and the neutron balance. For an heterogeneous core, the calculation of the va­riation of the spatial form of the flux with the cell compo--sition is of great importance for the calculation of the iso--topes burn-up. For fast reactors the variation of multigroup cross-sections as a function of the composition is also impor--tant. Therefore a multigroup calculation appears to be neces--sary. However, in order to use time constant cross-sections in the depletion equations (1), without neglecting the spectrum variation in the fuel element, the code assumes that the flux variation in the cell is function of the time averaged composi--tion in the cell itself, by means of the self-shielding fact--ors.

The self-shielding factors are defined as the ratio Let--ween the true reaction rate of the isotope considered and the reaction rate which would be obtained, if the flux in the cell was everywhere equal to a reference flux, say the flux at the cell boundary or the average flux in a given part of the cell.

If the group structure is sufficiently fine, the flux shape in the fuel element can be supposed to depend only on the macroscopic absorption cross-section of the cell in the energy group considered. In this case of spatially heterogene--ous cores few previous transport calculations for the same cell geometry with different compositions will enable to ob--tain a fitting of the self-shielding factors as a function of the cell absorption cross-section. A good fitting is given for example with the formula:

ς Q 0 " I E , i M I E , i

( 2 )

Ί + "alïï ^ 2 I E , i ' *" a l l í ' 3 I E , i

/

where S5rr-, . i ü . ü h o s e l f - s h i e l d i n g f a c t o r ox '"IE, , i ra

tl'!e i s o t o p e i i n t h e e n e r g y g r o u p

ν a j E i s t i ie t o t a l m a c r o s c o p i c a b s o r p t -

- i o n c r o s s - s e c t i o n of t h e c e l l i n

t h e g r o u p i E

TV TT-, · ; T„ -, ..; Τ.-,-,., ■ a r e t u e c o e f f i c i e n t s ί ΐ ιρυΐ i o d i n t o I 1 ili , 1 a 1 ¡-i f 1 j i υ , 1

the programme and are different i or

each. Piroirp and isotope.

- 8 -

4. '.'HE DIFFUSION CALCULATION METHOD

A diffusion calculation procedure not too time consuming but still accurate is needed, due to the fact that the, code has to perform many such calculations in a single run, taking in­to account the flux currents and the different flux levels in the various zones in which the reactor is subvided. An analytical nodal approach for the solution of the diffusion equation in one energy group is employed. (Ref.1) The basic idea is that the real spatial form of the flux within each region is uninteresting for the code purposes; only the ave­rage fluxes in each region are actually needed for the cal­culation, while the neutron currents between adjacent regions shalialso be correctly evaluated. The one energy group flux is the solution of the second order differential equation:

with v2*R + BR *R = ° ( 3 )

4 = <v 2fR-2aR)/DR (4)

The solution of such equation will require the determination of two functions of the boundary coordinates. In order to ar­rive to a simple solution, the approximation is made that the neutron currents are constant on each boundary of each region and equal to an average value. In this way the true "-two-dimension solution can be approximated by the superposi­tion of two one-dimension solutions and a total of four coef­ficients have to be determined (two for each direction). The two analytical functions which are solution of the equa­tion (3) in each direction depend on the component of the buckling Β in either direction (say α and β , where « +β = R ) If these quantities would be known, the four coefficients present in the flux solution for each zone could be expressed in terms of the average·fluxes in the zones. The solution of the equation (3) 'would then become an espres-sion of the type:

\|r..Z.. = E..\lf. „ · + F. . ψ. „ . + H..\lf. . „ + G : . \Ir . . /r.\

­ 9 ­

where ijrij are the region average fluxes, i and j are the in­

­dices of the r&actor regions. The programme starts guessing

the quantities «andßrand then solving the system (5); it ob­

­tains the average fluxes in each region and the flux curren­

t s between adjacent regions. At this point the two componen­

­ts of the buckling« and Fare recalculated and new coeffi­

cients for the expressions (5) are obtained. This leads to

a new solution for the average fluxes and the currents. When

this procedure has converged, the reactivity of the system

is calculated. If criticality is not achieved, the source

term is adjusted and the calculation is repeated till the

fluxes and the currents match with a critical system.

The procedure'described assumes the separability of the flux­

­es within each region. The inaccuracy due to this approxima­

tion has been verified to be of no major concern for the e­

­quilibrium fuel cycle calculations for the fast reactors,

although improvements can be searched for in this connection.

Finally the diffusion calculation in one energy group has

been demonstrated to give quite accurate results for this

kind of problems in power fast reactor. Figure 1. gives the

flux distribution in the radial direction calculated in one

energy group with the nodal approach and in 26 energy group

with the finite difference method diffusion code SQUID (Ref.

2). The agreement is satisfactory.

5. SPECTRUM CALCULATION AND BUCKLING VECTORS

The flux spectrum in each of the region in which the reactor

is subvided must correspond to a critical assembly. The spec­

­trum calculation will then be correct once proper values of

multigroup bucklings are introduced into the spectrum routine

for each region.

The buckling values supplied are the one deduced by the

one group diffusion calculation. The direct use of these va­

lues to describe the leakages can introduce an error into

the spectrum, as the energy dependence of the current;is not

properly taken into account by a(single value buckling. FOr

this reason provision is made to introduce into the program­

­me a set of previously calculated buckling vectorsV

With these quantities the energy group bucklings have to sa­

tisfy the equality:

,2 A / „.„ A ^ *2 Sum DIE BIE 0IE / Sum ^ I E = D Β ( 6 )

lb Ih

where

2 ­2 BIE ­

B VIE

- 10 -

which imposes that the total leakage has to remain the same. The energy group bucklings obtained from equalities (6) are supplied into the spectrum routine. When the calculation of the region spectra has converged, the programme uses the multigroup energy fluxes obtained to con­dense in one group the macroscopic quantities that have to be introduced into the one group diffusion equation (3)·

6. THE CALCULATION PROCEDURE

The programme flow diagram is shown in fig. 2 and 3· First the set of the library data is read in. These data con­sist in cross-section values, fission yields, the fission source spectrum, the convergence criteria, and the informations needed to generate the isotopes transmutation chains. Next information are those necessary to describe the reactor. The number of burnable regions, the dimensions of each region,the region compositions and the one group constant for the reflec­tor have to be provided. The information include the total thermal power of the reactor, the burn-up values for the regions, together with a guess for the axial blanket burn-up, or in turn the burn-up averaged along an axial stripe, and a guess for the feed quantity in the certain region which has been pre-determined for the search. To begin the calculation a flux distribution is guessed: flat in the radial direction and cosinus shaped in the axial direc­tion. The burn-up values of the axial regions are re-adjusted to give equal residence time in every axial stripe, or in turn region burn-up are calculated from the flux cosinus distribu­tion.

Region spectra are then computed from the fuel composi­tions given, taking also into account the fuel guess. Resi­dence times are calculated from the one group flux distribu­tion and the burn-up values obtained. Using these data pro­gramme estimates the average and final concentrations of each region. Region spectra and K-effee tive are then calcula­ted using the more recent average composition. Up to this point the flux spatial distribution has not been altered. Provision is made to recycle any fraction of any nuclide in the same or in another zonæ. If this is the case new initial concentrations are obtained adding the fraction of the recy­cled isotopes at the end of the burn-up to the original ini­tial densities. In any case the depletion and the spectrum calculation are repeated until the multiplication factors of the two consecuti­ve iterations differ by less than the corresponding convergence criterion.

- 11 -

This is the flux spectrum recycle loop and it has been dedu­ced mainly from the zero-dimensional burn-up code Gaffee (Ref. 3). At this point the code enters into the nodal calculation of the flux spatial distribution. With the new flux levels the resi--dence time values are re-adjusted in each zone. Next, the programme proceeds with the routine which calculates the reac­tivity at the beginning and at the end of the refueling in­terval. If the smaller of the two corresponding values of the multiplication factorsis within the specified convergen­c e criterion from the searched value, the code controls the residence time of the axial stripes and, eventually after another burn-up calculation in the case these time values have to be re-adjusted, the computation stops;-If the convergency on the K-effeetive is not achieved, the programme re-enters into the flux spectrum recycle loop and the calculation is repeated.

7. OUTPUT DESCRIPTION

The programme prints first of all the input data: the libra­r y nuclear data, the compositions of the regions and the geometry of the reactor. The iteration procedure can be easily followed in the output list. When convergence is achieved the initial average and the final isotopie compositions are printed together with spectra, macroscopic multigroup cross-section and neutron ba--lance for each region. Fraction of the power, power densities, specific power, ave--rage reactor conversion ratio and the doubling time of the system are also gixen. Finally a number of data are edited and punched on cards, which may be used if a calculation of the fuel cycle cost has tobe performed. These are: initial, average and final, fuel isotopie composition of each region, the region volume (in cm3) and the fuel residence time (in days), the fuel specific power (in watt/gr of fuel) and the power densities, (in watt/ /cm3). '

8. ACKNOWLEDGEMENTS

Thanks are due to Dr. Rinaldini for his const .ant support and his valuable suggestions.

- 12

9. REFERENCES

Ref. 1 C. Rinaldini - A nodal approach to solve few region neutron diffusion problems.

Energia Nucleare - Vol. 17 N.7 - Lu­glio 1970.

Ref. 2 SQUID - A multigroup program with criticality searches for the IBM - 360 - EUR 388 2C.

Ref. 3 GAFFEE - A G.G.A. zero dimensional equilibrium burn-up code.

Λ

^ 1 ΙΑ "c 3

£ S *-· 2 ι -Ο ^ /

Χ Ξ 0.5 LI­

CORE 1

—

,

CORE 2

V ν*

BLANKET REFLECTOR

One group nodal approach to the diffusion equation

?fi group f ini*» difference

calculation

Vv

Ι

NN. ^S^ ^ ν ^ • Ό ^ , ^

^̂ ^̂ ^̂ ^̂ ^̂

ι . . .

)

i I I W U ) . ^ B W J ~ . ^ = i

I I—' CO

50 100 150 200

Fig. 1 Radius (cm)

14 Read library data

Read case data

I Guesses on flux level,i-nitial and average densi-

I Self scbielding calcula-

I Compute flux spectra and Keff

Compute initial nu­clide con­centrations

Computers feed quanti­ty

.no

Burn-up calculation: com pute average and end of life isotopie density

I Self schielding calcula-° τ ion

Compute flux spectra and Keff'

no

Diffusion calcula-J tion 1 *

Residence time adjustment 1 ι

final. Κ eƒƒ· calculation

no

convergence on axial residence time

1 yes I Exit L

Fig. 2 - Programme flow diagram

­ 15

Adjust

the neutron

source

Guess on the buckling components

in the R,z directions

A d , l u s t

t h e bun'■<.! i n¿

Comp c n e n t s < n r >

1

Nodal coe f f i c i en t s ca l cu l a t i on

no

I Flux matrix

so lu t ion

I Compute the currents

Are the currents coherent

with the buckling componen­

ts?

yes

Fig. 3 - Diffusion calculation flow diagram

Word

Column

F o r m a t

Card

N° A1

Syrnbo 1

1

1-4

I n t e g e r

Number of e n e r g y g r o u p s

26

N26

2

5-8

I n t e g e r

Number of f a s t g r o u p s

24 '

N23

3

9 -12

I n t e g e r

Number of c r o s s s e c t i o n b l o c k s

40

NLB

4

13-16

I n t e g e r

Number of h e a v y n u c l i d e s

NHEV

•5 17 -20

I n t e g e r

Number of m o d e r a t o r n u c l i d e s

3

NLM

6

2 1 - 2 4

I n t e g e r

Dummy

NLT

Word

Column

F o r m a t

Card

N° A1 c o n t . )

Symbo1

7

2 5 - 2 8

I n t e g e r

Number of b u r n u p s t e p d e s c r i b e d i n t h e p r i n t o u t ( u s u a l l y = l )

NCOST

8 2 9 - 3 2

I n t e g e r

i d . number of t h e c o n -- t r o l ( s h o u l t be z e r o i f n< X e - o v e r . c a l c u l a t i o n i s d e s i r e d )

NBORON

9

3 3 - 3 6

I n t e g e r

i d . number of t h e

I Xe-135 i n ) t h e l i b r a r y

NXE5

CT> I

Word

Column

Format

Card

N° A2

Symbo 1

1

1-4

I n t e g e r

N u c l i d e number

L

2

5-8

I n t e g e r

N u c l i d e number of 1 s t c a p t u r e p a r e n t

NCAP1 (L)

3

9 - 1 2

I n t e g e r

N u c l i d e number of 2nd c a p t u r e p a r e n t

NCAP2 (L)

4

1 3 - 1 6

I n t e g e r

N u c l i d e number of N, 2N p a r e n t

NN2NN (L)

5

17 -20

I n t e g e r

N u c l i d e number of d e c a y p a r e n t

NBETA (L)

6

2 1 - 2 4

I n t e g e r

N u c l i d e h a s n o n - z e r o o f? 0 - No 1 - Yes

KFISS (L)

Comment

Supply one card for each nuclide.

Word.

Column

Format

Card tf° A2

( c o n t . )

Symbol

7

2 5 - 2 8

I n t e g e r

N u c l i d e i s a f i s s i o n p r o d u c t ?

0 - No 1 - Yes

KFP (L)

— 8

2 9 - 3 2

I n t e g e r

N u c l i d e h a s n o n - z e r o

? n , 2n 0 - No 1 - Yes

KN2N (L)

9

3 3 - 3 6

B l a n k

10

3 7 - 4 8

Dec ima l

Decay c o n s t a n t

XLAM (L)

11

4 9 - 6 0

Dec imal

L e a k a g e c o n s t a n t

XLEAK (L)

12

6 1 - 7 2

Dec imal

Atomic w e i g h t

AWT (L)

Word

Column

F o r m a t

Card.

N° A3

Symbo1

1

1-4

I n t e g e r

1st n u c l i d e i s p r imary f i s s i l e ? 0 - No 1 - Yes

NFA (1)

2

5-8

I n t e g e r 2nd n u c l i d e i s p r imary f i s s i l e ? 0 - No 1 - Yes

NFA (2)

3

9-12 I n - t e g e r

3rd n u c l i d e i s p r imary f i s s i l e ? 0 - No 1 - Yes

NFA (3)

4

13-16 I n t e g e r

e t c .

e t c .

5

17-20

Word.

Column

F o r m a t

Card.

N° A4

Symbol

1

1-4

In teger 1st nucl ide i s p r i m . f i s s precursor? 0 - No 1 - Yes

-1 Neg c o n t r i

NCR (1)

2

5-8

I n t e g e r 2nd n u c l i d e

. i s p r i m . f i s s p r e c u r s o r ? 0 - No 1 - Yes

bINeg c o n t r i b

NCR (2)

3 9-12

I n t e g e r

3rd n u c l i d e i s p r i m . f i s s p r e c u r s o r ? 0 - No 1 - Yes 1 Neg c o n t r i

NCR (3)

4

13-16

I n t e g e r

9

e t c .

D

e t c .

5

17-20

Comment

Supply one word of da t a f o r each heavy n u c l i d e . See card A1 word 4.

Cont inue on a d d i t i o n a l c a r d s i f n e c e s s a r y .

Comment 03 I

Supply one word of data for each heavy nuclide. See card A1, word4

Continue on additional cards if necessary.

Word

Column

F o r m a t

Card

A 5

Symbo1

1

1-12

Dec imal

F i s s . Y i e l d from 1 s t h e a v y

YIELD ( I , i ;

2

13-24

Dec imal

F i s s . Y i e l d from 2nd h e a v y

YIELD ( 1 , 2 )

3

2 5 - 3 6

Dec imal

F i s s . Y i e l d f rom 3 r d h e a v y

YIELD ( 1 , 3 )

4

3 7 - 4 8

Dec ima l

e t c .

e t c .

5

4 9 - 6 0

Comment

Supp ly a y i e l d v a l u e from e a c h h e a v y n u c l i d e . See c a r d A1 , word 4 . Supp ly y i e l d s

a s e t of f o r e a c h fi¡3

p r o d u c t . B e g i n e a c h s e t on a new c a r d .

See c a r d A2 ,word7

Word

Column

Format-

Car d.

A6

1

1-6

A l p h a n u m e r i c

N u c l i d e I d e n t i f i c a ­t i o n

2

7 - 6 0

A l p h a n u m e r i c

O t h e r c r o s s -b l o c k i d e n ­t i f i c a t i o n

3

60-64

I n t e g e r

0 - Not a m o d e r a t o r 1 - m o d e r a t o i

4

6 5 - 6 8

I n t e g e r

Read t r a n s f e r m a t r i x ? • 0 - Yes

1 - No

: Symbol I CLOG CK AME ¡ NMOD | MATRIX

5

6 9 - 7 2

I n t e g e r

" Read s e l f -s h i e l d i n g f a c t o r s 0 - No 1 - Yes

NSHLD

Comment Repeat cards A6, A7, A8, A9, and A10 in sets for each cross section .block. See card A1, word 3.

Word

Column

Format

Card

A7

Symbol

1

1-12

v c f

FISIG

2

13-24

°tr

TOSIG

3

25-36

°a

ABSIG

4

37-48

°g ,g+ l

OUSIG

5

49-60

V

XNU

•

6

61-72

° n , 2 n

XNSIG

Comment

Supply one card

for each energy

group.

See card A1,

word 1.

Word

Column

Format

Card

A 8

Symbo1

1

1-12

Decimal

0 τ

g>g+l

OUSIG

2

13-24

Decimal

σ g ,g+2

3

25-36

Decimal

g,g+3

4

37-48

Decimal

e t c .

5

49-60

Decimal

• · · ·

6

61-72

Opt imal

σ, l a s t g fas t

group

to

o

Comment

Fast group transf(¡r

matrix;Start a new

,card for each

group.

Continue on another

card if necessary.

Supply this data

for all fast grou]j>

except the last.

Word

Column

Format

Card A9

Symbo1

' 1

1-12

Dec ima l

6 . , 1 s t ë t h e r m a l

g r o u p

OUSIGM

2

13 -24

Dec ima l

Co., 2nd t h e r m a l g r o u p

3

2 5 - 3 6

Dec ima l

o ¿ , 3 r d & t he rmal

group

4

37-48

Decimal

e t c .

5

49-60 Decimal

• · · ·

6

61 -72

Dec ima l

O), , l a s t ° t h e r m a l

g roup

OUSIGM

Comment Transfer into thermal region for moderators only: Start a new card for each group. Supply this data for all fast and thermal groups.

Word

Column

Format

Card A10

Symbo1

1

1-12

Dec ima l

F i s s i o n s o u r c e f r a c t i o n f o r 1 s t g r o u p

CHI(1)

2 "

13-24

Dec ima l

F i s s i o n s o u r c e f r a c t i o n f o r 2nd g r o u p

CHI(2)

3

2 5 - 3 6

Dec ima l

F i s s i o n s o u r c e f r a c t i o n f o r 3 r d g r o u p

CKI(3)

4

3 7 - 4 8

Dec ima l

e t c .

5

4 9 - 6 0

Dec ima l

• * · ·

6

61-72 Decimal

F i s s i o n source f r a c t i o n f o r l a s t group

CHI(N26)

Comment Supply a value for each group, including thermal groups.

Continue on additional cards if necessary.

Word j 1

Column

Format

Card A11

Symbo1

1-12

Decimal

Flux convergeance c r i t e r i o n

2 ί 3 i 4

13-24 I 25-36 I 37-48 ! ! i

Decimal ! Decimal ' Decimal

F l u x - r e c y c l e loop conver ­gence c r i t e r i o n

CONK EPS1

F i n a l h „„ eff convergence c r i t e r i o n

EPS2

F r a c t i o n of power r e d u c t i o n fo r X e - o v e r r . c a l c u l a t i o n

Comment

CM CO PH w V τ— CO FH W V

o o

ΙΓΝ O o O •

m o o o

•

o o o o •

CD H PH

CO Χ ω fH o

t p

Word.

Column

Format

Card 1 Β

j Symbol

1

1-4

I n t e g e r

Number of s e l f s h i e l d i n g s e t to be supp l i ed ( i f zero sk ip to card 1)

. , , !

— — ■■ " j

NSET | j |

,ο,α I 1 I

­,

- -

Format,

η .3 -,-. -̂

2 3

Symbo1

1­4

Integer

set number

I

2

5­8

Integer

=0 fitting

on concen­

tration

formula (ï)

=1fitting

on concentr.

formula (.2)

>1 see next

word

NJZSPT(I)

3

7­12

Integer

=0 fitting

on a

formula (1)

=1 fitting

on a

formula (2)

4

13­16

Integer

id. number

of the 1st

isotope

referred'by

N$PT=0 or

N0PT=1

N#PI(I) i IS(I,1)

5

17­20

Integer

id. number

of the 2nd

isotope

referred by

N$PT=0 or

N$PT=1

is.CU.2l

6

21­24

Integer

id. number

of the 3rd

isotope

referred by

N#PT=0­ or

N$PT=1

_x_sjtxai . .

■." _'■ Γ' I

, . , _ .

i' 0 .7'■'.. -i ί.

3 Β

Symbo1

1 2 1-12 13-24

Decimal First coefficient group ( 1 ) formula (1)

Decimal Second coefficient group ( 1 ) formula ( 1 )

3 25-36

Decimal Third coefficient group ( 1 ) formula (ï)

4 37-¿3

Decimal First coefficient group (2) formula (1)

T1(I,1) ¡ T2(I,1) T3(I,1) I T1(I,2)

5 42-60

Decimal Second coefficient group (2) formula (1)

T2(I,2)

6 61-72

Decimal Third coefficient group (2) formula (1)

T3(I,2)

Comment only if

NSET> 0 (as many) (as NSET)

CO CO

Comment Only i f N#PT = 0 or NJØPT 1 and Nj#PI = 0 c o n t i n u e on a n o t h e r ca rd i f n e c e s s a r y .

Word

Column

Format

Card.

4 Β

Symbo1

1

1-12

Decimal

F i r s t c o e f f i c i e n t

group(1)

formula (2)

S1 (1 ,1 )

2

13-24

Decimal

Second c o e f f i c i e n t

group (1)

formula (2)

S2 (1 ,1 )

3

25-36

Decimal

t h i r d c o e f f i c i e n t

group (1)

formula (2)

S3 (1 ,1 )

4

37-48

Decimal

4 t h

S4 ( 1 . 1 )

5

49-60

Decimal

5 t h

S5 ( 1 . 1 )

6

61-72

Decimal

6 t h

S6 (1 ,1 ) .

Comment

Only i f NJ&PT or NJ&PT 1 NØPI = 1

c o n t i n u e : 1 card each t

= 1

group

Word.

Column

Format

Card

5 B

Symbo1

1

1-12

Decimal

Cons tan t

s e l f

s h i e l d i n g

s e t i

group 1

S S ( i , l )

2

13-24

Decimal

group 2

S S ( i , 2 )

3

25-36

Decimal

group 3

4

37-48

Decimal

group 4

5

49-60

Decimal

group 5

6

61-72

Decimal

group 6

- -

—

N3

Comment

Only i f

NSET<0 c o n t i n u e on a n o t h e r card

n e c e s s a r y .

i f

Vio rd

Column

Format

Card

6 Β

Symbo1

• 1

1-4

In teger Id. number of the se l f sh ie ld ing se t for isotope 1

ISET (1)

2

5-6

In teger Id. number of the se l f sh ie ld ing se t for isotope 2

ISET (2)

3

7 - 8

In teger

e t c .

ISET (3)

I

t

Comment

Word

Column

Format

Card.

N° 1

Symbo1

1

1-72

A l p h a n u m e r i c

Case i d e n t i f i c a ­t i o n

—

Supply as many words as word 3 card A1; continue on another card if necessary

CO CJ1

ί Kord I

Formot

Card

N° 2

Symbo1

1

1-4

I n t e g e r

Number of n u c l i d e c a r d s t o be r e a d ( c a r d 6)

NREAD

2

5-8

I n t e g e r

0-No e f f e c t N-Punch

w e i g h t s f o r Ν t i m e i n t e r v a l s

NCOST

3 9-12

I n t e g e r

S e a r c h o p t i o n O-Feed q u a n t i t y 1 - b u r n - u p . (MWD/T)

ΝΤΥΡΕ

4

13-16

I n - 1 eg e r

Number of r e l o a d i n t e r v a l s d u r i n g l i f e on one b a t c h

IRELO

5 17-20

I n t e g e r

Maximum t o t a l i t e r a t i o n s

JNSTOP

6

2 1 - 2 4

I n t e g e r

Maximum i t e r a t i o n s ' i n a s i n g l e f l u x - r e c y c l e l o o p

JNNSTP

Wo ^ d

Column

F o r m a t

C^rd.

N° 2

Symbol

7

25-28 In teger

0-No ef fec t 1-Search

for recycle f ac to r i f necessary

JNESTP I

Word

Column

Format

Card

N° 2

c o n t . )

Symbo1

' 8

2 9 - 3 2

I n t e g e r

0-No e f f e c t

1-punch

a tom

d e n s i t i e s

NPUN

9

3 3 - 3 6

I n t e g e r

l i b r a r y

f o r n e x t

c a s e

O-Same

1-Read AI-A12

1-Read A l l -

-A12

NLI3

10

3 7 - 4 0

0-No e f f e c t

1 -Po i son

o r f e r t .

m a t .

s e a r c h

NFIXPO) • · · ·

18

69-72

In teger

NFIXP(9)

Word.

Column

Format

Card

N° 3

Symbol

1

1-4

I n t e g e r

Number of

r a d i a l

b u r n a b l e

z o n e s

NZØNE

2 ~

5-8

I n t e g e r

Number of

a x i a l

b u r n a b l e

z o n e s

NZETA

3

7 -12

I n t e g e r

i s t h e

s e a r c h t o be

p e r f o r m e d i n

zone 1?

1 y e s

0 n o

ICHANGO)

4

13-16

I n t e g e r

s u p p l y a s

many words

a s word 1

• · * ·

ICHANG(2)

5

17 -20

I n t e g e r

ICHANG

6

2 1 - 2 4

I n t e g e r

b u c k l i n g

o p t i o n i f ? 0

t h e one ρ g r o u p B'~

w i l l be

s h a r e d among

t h e g r o u p s

NVECT

Word

Column

Format

Card

N° 3 (con t . )

Symbol

7

2 5 - 2 8

I n t e g e r

h a s t h e c a l ­c u l a t i o n t o be p e r f o r m e d w i t h an a v e r a ge a x i a l

b u r n - u p ? 1 no 0 y e s

NBR

! , I

!

Word

Column

Format

Card

N° 4

Symbol

1

1-12

Dec ima l = 0

a x i a l symmetry

= 1 no symmetry

i n a x i a l d i r e c t i o n

HEIGHT

2

13-24

Dec imal 1 g roup d i f f u s i o n c o e f f i c i e n t of t h e r e f l e c t o r

DREFL

3

2 5 - 3 6

Dec ima l

m a c r o s c o p i c a b s o r p t i o n x - s e c t i o n of t h e r e f l e c t o r

SAREFL

4

3 7 - 4 8

Dec ima l

f i s s i o n p e r w a t t s e c

FIWATT

5 4 9 - 6 0

Dec ima l

c o r e power ( w a t t s )

PØWER

6

61-72

Dec imal

s h u t - d o w n

e f f

ZKMIN

Word

Column

Format

Card

N° 5

Symbo1

Ί 1-12

Decimal

Minimum feed q u a n t i t y or burn-up

v a l u e

FMIN

2

13-24 Decimal

Maximum feed q u a n t i t y or burn-up

v a l u e

FMAX

3 25-36

Decimal

IF = 0 .0 DELTFD =1;5 ( IF χ 0) MINIF

( x , 1 . 5 )

DELTFD FLOATPd) FL0ATP(2) FL0ATP(3)

Comment

See c a r d 2 , w o r d 3 .

Word

Column

Format

Card

N° 6

Symbol

1

1-12

Decimal

r a d i u s (cm) of the f i r s t zone

RZjZfNEd)

2

13-24

Decimal

supply as many words a s NZJØNEH-1

RZJ0NE(2)

3 25-36

Decimal

e t c .

RZJ0NE(3)

to CO

Word

Column

Format

Card

N° 7

Symbo1

1

1-12

Dec imal

a x i a l t h i c k n e s s of t h e f i r s t zone (cm)

ZZ(1)

2

13-24

Dec ima l

s u p p l y a s many words a s NZETA4-1

ZZ(2)

3

2 5 - 3 6

Dec ima l

e t c .

ZZ(3)

Word

Column

Format

Card

Symbo1

1

1-12

Dec ima l

b u r n - u p (MWD/T) of t h e f i r s t r a d i a l and a x i a l zone

BRUP(1,1)

2

13-24

Dec ima l

s e c o n d r a d i a l z o n e f i r s t a x i a l zone

BRUP(2,1)

3

2 5 - 3 6

Dec ima l

s u p p l y a s many w o r d s a s NZ^NE t i m e s NZETA e t c .

N.B. The burn-up values of the first axial region are taken as average b.u. in axial direction when NBR=0.

o ί I

Word

Column

Format

Card

N° 9

Symbol

' 1

1-12

Dec ima l

r e s i d e n c e t i m e g u e s s ( d a y s ) f i r s t r a d i a l and a x i a l zone

DELDAY(1,1)

2

13-24

Dec ima l

s e c o n d r a d i a ! f i r s t a x i a l zone

DELDAY(2,1)

3

2 5 - 3 6

Dec ima l

. a s many w o r d s a s NZ$NE t i m e s NZETA

DELDAY(3,1) ; ! I

CO

Word.

Column

Format

Card

N° 10

Symbo1

1

1-12

Dec ima l

f e e d g u e s s 1 s t zone

FEED(1,1)

2

13-24

Dec ima l

FEED(2,1)

3

2 5 - 3 6

Dec ima l

a s amny w o r d s a s ΝΖ$ΝΕ t i m e s NZETA

FEED(3,1)

Word

Column

Format

Card

N° 11

Symbo1

1

1-12

Dec ima l

V e c t o r f o r r a d i a l b u c k l i n g 1 s t g r o u p

VECTjc5R(l)

2

13-24

Dec imal

V e c t o r f o r r a d i a l b u c k l i n g 2nd g roup

VECTJ0R(2)

3

2 5 - 3 6

Dec ima l

• · · ·

4

3 7 - 4 8

Dec ima l

• · · ·

-

5

4 9 - 6 0

Dec ima l

• · * ·

6

6 1 - 7 2

Dec ima l

V e c t o r f o r r a d i a l b u c k l i n g l a s t g r o u p

VECT$R(N26;

Comment

Continue on another card if necessary. As many vector sets as NZØNE. Only if word 5 card 3 is not 0.

Word

Column

Format

Card

N° 12

Symbo1

1

1-4

I n t e g e r

N u c l i d e i d e n t i f i c a ­t i o n number

L

2

5-8

I n t e g e r

0-No e f f e c t N-add r e ­

c y c l e d p a r t i n t o n u c l i d e N

NSWIT(L)

3

9 -12

I n t e g e r

t h e r e c y c l e d n u c l i d e i s i n t h e zone NSHU

NSHU

4

13-24

Dec ima l

R e c y c l e f r a c t i o n

QR(L)

5

2 5 - 3 6

Dec ima l

Feed f r a c t i o n

Z(L)

6

3 7 - 4 8

Dec ima l

C o n s t a n t f e e d q u a n t i t y ( a t o m s : b a r n - c m )

CDEN(L)

i Comment

Supp ly a s many n u c l i d e c a r d s a s r e q u i r e d .

See c a r d 2 , word 1. (As many s e t s a s t h e t o t a l numb e r of b u r n a b l e z o n e s )

Word

Column

Format

Card

N° 13

Symbol

Ί 1-4

I n t e g e r

Number of Th-232 n u c l i d e s

NW(1)

2

5-8 I n t e g e r

Number of f e d U-233 n u c l i d e s

NW(2)

3 9 - 1 2

I n t e g e r

Number of f e d U-235 n u c l i d e s

NW(3)

4

1 3 - 1 6

I n t e g e r

Number of f e d P u - 2 3 9 , P u - 2 4 1 , and Np-239 n u c l i d e s

NW(4)

5 17-20

I n t e g e r

Number of b r e d P a - 2 3 3 and U-233 n u c l i d e s

NW(5)

6

2 1 - 2 4

I n t e g e r

Number of b r e d U-235 n u c l i d e s

NW(6)

Comment

Supp ly a s e t of c a r d s 7 and 8 i f f u e l w t s . a r e t o be p u n c h e d . See c a r d 2 .

Supp ly a s e t of ci and 8 i f

2 , word

s e c o n d a r d s 7

t h e r e a r e two f u e l p a r t i c l e t y p e s .

Word

Column

Format

Card

N° 13 (con t . )

Symbol

7 25-28

I n t e g e r

Number of b r e d N p - 2 3 9 , P u - 2 3 9 , and P u - 2 4 1 n u c l i d e s

NW(7)

8 29-32

I n t e g e r

Number of a l l U-232 n u c l i d e s

NW(8)

9 33-36

I n t e g e r

Number of a l l P a - 2 3 3 and u r a n i u m n u c l i d e s

NW(9)

10

3 7 - 4 0

I n t e g e r

Number of a l l Np-239 and p l u t o n ­ium n u c l i d e s

NW(10)

11

4 1 - 4 4

I n t e g e r

Number of f u e l p a r t i ­c l e s 0 - 1 p a r t i c l e 1-2 p a r t i c l e s

NPT

Word

Column

Format

Card

N° 14

Symbo1

1 ,

1-4 Integer

Ident. no. of 1st nuclide referred to by card 7

LISTO)

2

5-8

Integer

Ident. no. of 2nd nuclide referred to by card 7

LIST(2)

3

9-12 Integer

Ident. no. of 3rd nuclide referred to by card 7

LIST(3)

4

13-16 Integer

etc.

etc .

Word

Column

Format

Card

Symbo1

Comment

List the identi­fication number of each nuclide referred to by card 7, words 1 to 10.

Continue on another card if necessary.

(As many sets as the total number of burnable zones)

CO

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