ATOMIC ENERGY Vs33 L'ENERGIE ATOMIQUE OF CANADA LIMITED … · ATOMIC ENERGY Vs33 L'ENERGIE ATOMIQUE OF CANADA LIMITED W^^W DU CANADA ... Ce code §crit en FORTRAN V est ... MICRETE

AFCL-7679

ATOMIC ENERGY V s 3 3 L'ENERGIE ATOMIQUE

OF CANADA LIMITED W^^W DU CANADA LIMITEE

MICRETE VERSION 4.1

USER'S MANUAL AND PROGRAM DESCRIPTION

MICRETE Version 4.1

Mode d'emploi et description du programme

R.A. JUDD

Chalk River Nuclear Laboratories Laboratoires nucleaires de Chalk River

Chalk River, Ontario

] July 1982 juillet

ATOMIC ENERGY OF CANADA LIMITED

MICRETE Version 4.1User's Manual and Program Description

by

R.A. Judd

Applied Mathematics BranchChalk River Nuclear Laboratories

Chalk River, Ontario KOJ U O1982 July

AECL-7679

L'ENERGIE ATOMIQUE DU CANADA, LIMITEE

MICRETE Version 4.1

Mode d'emploi et description du programme

par

R.A. Judd

MICRETE Version 4.1 est un code pour les rfiacteurs het§rogenes,du type zone source - zone d'absorption, qui rSsout 1'equation dediffusion des neutrons en deux groupes et en deux dimensions dans lagSomgtrie carrfie ou hexagonale. Ce code §crit en FORTRAN V estexploitable sur 1'installation CRNL 6600/Cyber 170.

Dfipartement de mathe"matiques appliqu§esLaboratoires nuclfisires de Chalk River

Chalk River, Ontario KOJ 1J0

Juillet 1982

AECL-7679

ATOMIC ENERGY OF CANADA LIMITED

MICRETE Version 4.1User's Manual and Program Description

by

R.A. Judd

Abstract

MICRETE Version 4.1 is a heterogeneous source-sink reactorcode that solves the static neutron diffusion equation in twogroups and two dimensions in either square or hexagonalgeometry. It is written in FORTRAN V and is operational on theCRNL 6600/Cyber 170 computer system.

Applied Mathematics BranchChalk River Nuclear LaboratoriesChalk River, Ontario KOJ 1J0

1982 July

AECL-7679

MICRETE Revision Record

Date Revision Description

82-05-15 Version 4.1 Original release

Table of Contents

page

1. General Introduction 1-11.1 About MICRETE1.2 Acknowledgements1.3 About this Report

2. MICRETE Program Abstract 2-1

3. Running MICRETE 3-13.1 Input Data Description3.2 Output Interpretation3.3 Sample Problems

4. Model Equations and Associated Calculations 4-14.1 Model Equations and their Solution4.2 Buckling Calculations4.3 Surface Flux Calculations

5. Program Description 5-15.1 Subprogram Descriptions5.2 Memory Limitations

Appendix A - Program Maps A-l

Appendix B - Program Source Listing B-l

List of Tables

page

Table A-l Subprogram Call Map A-3

Table A-2 Common Block Map A-4

Table A-3 Symbol Map A-5

List of Figures

page

Figure 3-1 Typical Job Deck 3-7

Figure 3-2 Output from Typical Job 3-7

Figure 3-3 Substitution Experimental Analysis

Job Deck 3-11

Figure 3-4 Output from Substitution ExperimentAnalysis 3-12

Figure 5-1 Program Hierarchical Diagram 5-4

1 - 1

1. General Introduction

1.1 About MICRETE

The original version of MICRETE, a two-dimensional, two-groupheterogeneous source-sink reactor code, was developed byJ.D. Stewart and implemented hy J.M. Kennedy and S.J. Cowley inthe early 1960's. Since v.he' MICRETE has undergone severalrevisions, the most significant of which occurred with thedevelopment of MICRETE Version 4.0. In Version 4,0, the theorywas modified to reproduce flux distributions more realistically,to include a radial reflector having properties different fromthose of the moderator and to better represent cores havingasymmetric fuel loadings.

Since the early 1960's, the various versions of MICRETE havebeen used extensively to model ZED-2 reactor operation and toanalyse so-called 'substitu:ion' experiments. The currentversion, Version 4.1, not only includes all the features ofVersion 4.0 but also includes features that automate'substitution' experiment analysis.

1.2 Acknowledgements

J.D. Stewart originally developed the 'MICroscopic-discRi.TE'theory in the early 1950's. Since then he progressivelyextended the theory until his retirement in 1971. The originalG-20 version of MICRETE was written by J.D. Stewart andJ.M. Kennedy with assistance from Mrs. S.J. Cowley. Since thenMICRETE has been converted to FORTRAN and modified by C. Tannerand F. McDonnell with assistance from H.E. Sills, L. Hansen,R. Cranston and R. Blain. This report has borrowed extensivelyfrom reports and other documents generated by those mentionedabove.

I am particularly grateful to J. Griffiths and A. Okazaki forhelpful discussions and to G. Mascarin who assisted with thetesting of MICRETE Version 4.1.

1.3 About this Report

Section 2, MICRETE Program Abstract, provides a summary ofMICRETE capabilities and implementation requirements. Itcontains enough information to permit the reader to assess theapplicability of MICRETE to his needs. All supporting referencematerial is listed in this section.

Section 3, Running MICRETE, is the so-called 'User's Manual*.User input and MICRETE output are described. Sample problemsare also provided.

1 - 2

Section 4, Model Equations and Associated Calculations, andSection 5, Program Description, combined with the program mapsand source listing reported in Appendices A and B provide theinformation necessary to understand MICRETE Version 4.1 programinternals.

2 - 1

2. PROGRAM ABSTRACT

2.1 PROGRAM NAME or DESIGNATION - MICRETE Version 4.1

2.2 COMPUTER FOR WHICH PROGRAM IS DESIGNED AND OTHERS UPONWHICH IT IS OPERABLE - CDC 6600, CDC Cyber 170 Model 175

2.3 NATURE OF PROBLEM SOLVED - The static neutron diffusionequation is solved in two groups and two dimensions in eithersquare or hexagonal geometry.

2.4 METHOD OF SOLUTION - The 'microscopic-discrete' theorydeveloped by J.D. Stewart1'2 is applied to the neutron diffusionequation. The resultant eigenvalue problem is solved byadjusting the problem eigenvalue until the determinant is'aero1. Having determined the problem eigenvalue, flux shapesare computed from model equations.

2.5 RESTRICTIONS ON PROBLEM COMPLEXITY

i - Fixed array dimensions limit the size and complexityof the lattice that can be modelled without recompiling MICRETE.

ii - Geometry is limited to square and hexagonalarrangements.

2.6 TYPICAL RUNNING TIME - On the CDC Cyber 170 Model 175,CP time required is approximately 10 milliseconds per rod periteration. The number of iterations is problem dependent.

2.7 UNUSUAL FEATURES OF PROGRAM - This program has beenspecially adapted to facilitate 'substitution' experimentanalysis.

2.8 RELATED AND AUXILIARY PROGRAMS'- None.

2.9 STATUS - Operational. The MICRETE code absolute,relocatable binary and source in UPDATE program library formatare disk resident on the CRNL computers under the designation:

MICRETE41, ID=JUDD

The highest cycle of this permanent file contains the currentabsolute followed by the binary and program library. Backupcopies of this cycle are recorded on the labelled 9-track tapesJ00677 and J00678 at 1600 cpi in SI format.

2.10 REFERENCES

1 - Stewart,J.D., 'A Microscopic-Discrete Theory ofThermal- Neutron Piles', Atomic Energy of Canada LimitedResearch Company, AECL-1470 (1962 March)

2 - 2

2 - Stewart,J.D., 'MICRETE 4 - Basic Theory1, AtomicEnergy of Canada Limited - Research Company, AECL-4053 (1971September)

3 - Stewart,J.D., Kennedy,J.M. and Cowley,J.S., 'MICRETE -A G-20 Program for Calculation of Finite Differences by theMicroscopic- Discrete Theory', Atomic Energy of Canari? Limited -Research Comnfjny, AECL-2547 (1966 February)

4 - McDonnell, F.N. and Tanner , C , 'MICRETE 4 User'sManual1, Atomic Energy of Canada Limited - Research Company,AECL-4155 (1972 March)

5 - Judd,R.A., 'MICRETE Version 4.1 - User's Manual andProgram Description1, Atomic Energy of Canada Limited - ResearchCompany, AECL-7679 (1982 May)

6 - Judd,R.A. and Mascarin,G., 'MICRETE Version 4.1Program Verification1, Atomic Energy of Canada LimitedResearch Company, CRNL-2372 (1982 April)

2.11 MACHINE REQUIREMENTS

The current version requires 143,000g (51,OOO^o) words ofcentral memory and access to nine sequential disk files.

2.12 PROGRAMMING LANGUAGES USED - FORTRAN V, the CDCimplementation of FORTRAN 77

2.13 OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM ISEXECUTED - NOS/BE Version 2.1

2.14 ANY OTHER PROGRAMMING OR OPERATING INFORMATION ORRESTRICTIONS - None.

2.15 NAME AND ESTABLISHMENT OF AUTHORS or CONTACT PERSONS

Ross A. JuddAdvanced Projects and Reactor Physics DivisionAtomic Energy of Canada Limited, Research CompanyChalk River, Ontario KOJ 1J0

Telephone: (613) 687-5581

2.16 MATERIAL AVAILABLE

i - User's Manual and Program Descriptioni i - Program test problems

2 - 3

2.17 KEYWORDS

Diffusion equationMicroscopic-discreteHeterogeneous reactorSource-sink

3 - 1

one illustrateda job consistscard and controlcall it intoinput. In thispermanent file

3. Running MICRETE

To run MICRETE, a batch job, similar to thein Figure 3-1, is submitted for execution. Suchof two sections. Section 1 contains the jobcards used to attach the MICRETE program andexecutior. Section 2 contains the MICRETE userexample, the MICRETE absolute, stored in theMICRETE41, is load<- . and executed.

3.1 Input Pat Description

MICRETE i'put consists of two types of information: 1)program directives and 2) directive data. The programdirectives - SELECT, DEFINE, MODIFY, SUBSTITUTE, RECALL, EXECUTEand END - direct and re-direct MICRETE program processing .

3.1.1 SELECT Directive

Upon encountering a SELECT directive, MICRETE reads directivedata stored on the next two cards. The first selects by nameeither the 'regular' or 'substitution' calculation mode(Section 3.3 - Sample Problems). The second provides the datarequired to size and partition variable dimension memory (*** inthis version, the second card must be BLANK as this feature isnot yet operational. * * * ) .

3.1.2 DEFINE Directive

Encountering a DEFINE directive causes MICRETE to read e newproblem definition. Once all problem definition data have beenprocessed the current definition is copied to the logical file,TAPE10, from where it can be retrieved by the RECALL directive.

To facilitate MODIFY and SUBSTITUTE directive processing,DEFINE directive data is divided into volumes, records andfields as follows:

Volume 0 — Descriptive title— FORMAT(A80)

Record 1jTield 1 - TITLE, problem descriptive titleField 2 - STITLE, problem descriptive sub-title

Volume 1 — Lattice description and calculation control data— FORMAT(5F15.8)

Record 1 -- Lattice dataField 1 - TRYY, interstitial factor for typical rodField 2 - BCE, measured reference lattice buckling. This

value is used only when a 'substitution'calculation is being performed.

Field 3 - BAA, i: lot equal to zero, alternate slowing downis omicced from resonance escape probability

3 - 2

Field 4

Field 5

Record 2 •Field 1

Field 2Field 3

Field 4Field 5

Record 3 •Field 1

iteration for type ITER fuel. This value is usedonly when a 'substitution' calculation is beingperformed.SURF, normally blank; if it is set to 1.0, rodsurface fluxes are calculated.PPOW, normally blank; if it is set to 1.0, rodpowers are calculated.

Geometric propertiesLATARNG, lattice arrangement, 90 for square and60 for hexagonalLAM, lattice coordinate spacing (cm)•SP, symmetry parameter:

0 - all points distinct1 - rotational symmetry, sixfold for hex-

agonal arrangement and fourfold forsquare arrangement

2 - reflectional symmetry, twelvefold forhexagonal arrangement and eightfold forsquare arrangement

3 - reflectional symmetry about the ordinateaxis, Q

H, extrapolated height (cm)RCOR, core radius (cm). If zero, the programcalculates the radius.

Iteration parameter control dataPARAMj iteration parameter:

0, 123

Field 2Field 3Field 4Field 5

Field 6

Field 7

iterate on eigenvalue, 1/(EKEFF)iterate on extrapolated heightiterate on resonance escape probabilityof type ITER rod. If p of type ITERrod is 1.0, then the iteration iseffectively on ETA of the type ITERrod.iterate on axial diffusion area of typeITER roditerate on core radiusiterate on outer radius of inner reflector

ITER, type number of type ITER rodsEKEFF, estimate of keffINC, iteration parameter initial incrementLCRIND, 'regular' calculation, level coefficientof reactivity calculation switch (1=ON, 0=OFF) ORINCS, 'substitution' calculation, substituted latticeiteration parameter initial increment.INCT, 'substitution' calculation, test lattice iter-ation parameter initial increment.INCTL, 'substitution' calculation, large test latticeiteration parameter initial increment

4 -

56

3 - 3

Record 4Field 1Field 2Field 3Field 4Field c __

Record 5 •Field 1Field 2Field 3Field 4Field 5

Moderator propertiesDF, fast diffusion coefficient (cm)D, thermal diffusion coefficient (cm)LSSQM, slowing down area (cn**2)LSSQC, typical cell slowing down area (cm**2)LSQM, diffusion area of moderator (cm**2)

Reflector propertiesDFR, fast diffusion coefficient (cm)DR, thermal diffusion coefficient (cm)LSSQR, slowing down area (cm**2)LSQR, diffusion area (cm**2)RP, outer radius of inner reflector (cm)

Record 6 — Outer reflector boundary conditions andbuckling control

Field 1 - ALPHAF, fast flux boundary condition:-1 - perfect reflector0 - black boundary

Field 2 - ALPHA, thermal flux boundary condition (as perField 1)

Field 3 - IP1, coordinate of the first buckling pointField 4 - IP2, coordinate of the second buckling pointField 5 - IP3, coordinate of the third buckling pointNote — if IP1 is -1, fit is performed on the first three

position records. If IP1, Ip2 and IP3 are zerothen IP1 is set to 1, IP2 to 2, and IP3 to 3.

Volume 2 — Rod and cell property data— FORMAT(I2,A10,F8.5,6F10.5,/,10X,4F10.5)

through nTY, type numberRODID, identifier (max 10 chars)RODRAD, radius (cm)GNOT, ratio of surface to average thermal fluxKINF, k-infinityPP, resonance escape probabilityLFCRSQ, radial slowing down area (c;n**2)LFCASQ, axial slowing down area (cm**2)LSQ, diffusion area (cm**2)F, interstitial factorFROD, thermal utilization factorFF, fuel thermal utilization factor. This valueis used only when powers are calculated.

Field 13 - FN, fuel power factor in units of power/thermalneutron absorbed. This value is used only whenpowers are calculated.

Note — Volume 2 input is read until a BLANK card isencountered.

RecordFieldFieldFieldFieldFieldFieldFieldFieldFieldFieldFieldField

1 t123456789101112

3 - 5

data are added to the current set. If the rod type is 0, theindicated rod information is deleted from the current set.Modifications are read until a BLANK card is encountered. LikeMODIFY changes, SUBSTITUTE modifications are cumulative. Toreturn to the currently defined reference problem, the RECALLdirective must be used.

Large lattice rod position data, entered under the SUBSTITUTEdirective, are combined with the reference lattice position datato define the large test lattice. These data are entered likeVolume 3 rod position data (Section 3.1.2, page 3-4). Each cardcontains up to 5 sets of position data, FORMAT(15F5.0). Datasets are read ur.til a BLANK card is encountered. If no dataprecede the BLANK card, the current large lattice data areretained.

3.1.5 RECALL Directive

Encountering the RECALL directive cau~-~ MICRETE to recallthe most recent problem definition written to i«_-.J'10, Thus if auser wishes to negate the cumulative effect of a series ofMODIFY nnd/or SUBSTITUTE modifications, he must make appropriateuse of this directive. There are no data associated with thisdirective.

3.1.6 EXECUTE Directive

Encountering this directive causes the current problem asmodified by MODIFY and/or SUBSTITUTE directives to be solved.

MICRETE to terminate

3.1.7 END Directive

Encountering the END directive causesall processing.

3.2 Output Interpretation

Executing the MICRETE job illustrated in Figure 3-1 causesthe output displayed in Figure 3-2 to be generated.

The first page of output is a copy of user input. Shoulderrors occur while MICRETE is processing user input, MICRETEwill attempt to identify the input data in error by issuing adiagnostic containing an error message, the card number and acopy of the card with which the error is associated.

Subsequent output contains an interpreted summary of eachproblem being solved, solution time warning errors and/or fatalerror diagnostics followed, if possible, by the problemsolution.

3 - 6

3.3 Sample Problems

3.3.1 REGULAR MICRETE

The typical MICRETE job illustrated in Figure 3-1 isrepresentative of calculations performed under the 'regular'calculation mode. In this case, a 121 rod ZED-2 lattice ofCANDU fuel is modelled and the assembly level coefficient ofreactivity calculated.

3.3.2 SUBSTITUTION MICRETE

To illustrate how MICRETE can be used to analyse a'substitution' experiment, consider the following experiment. Areference lattice consisting of 121 rods has an extrapolatedcritical height of 224.736 cm and an experimental buckling of3.8500 m~2. Seven rods of 19-element UO2 test fuel cooled withHB40 organic are substituted into the reference lattice. Theextrapolated critical height of the substituted lattice ismeasured and found to be 237.954 cm. Estimate the test fuelmaterial buckling and k-infinity.

The MICRETE job illustrated in Figure 3-3 when executedperforms the desired calculations. The solution generated bythis job is reported in Figure 3-4.

From Figure 3-4, we see that a 'substitution' calculation isin reality just a series of 'regular' calculations. The firstmodels the reference lattice by adjusting the reference (type 1)fuel resonance escape probability until the reference lattice Jn

buckling matches the experimental value. The second models thesubstituted lattice, adjusting the test fuel resonance escapeprobability until the computed critical height matches theexperimental value. The third predicts the performance of areactor loaded with test fuel. From this calculation, the testfuel Jgr Jn+I0 an^ material bucklings, and k-infinity areestimated.

The warnings issued following the failure of the small testlattice calculation, Figure 3-4, page 3-20, are representativeof MICRETE error diagnostics. In this case, the failure of thesmall test lattice calculation and an inconsistency in the largetest lattice rod position and symmetry data are noted. Indeed,careful examination of the position data, given the specifiedsymmetry, indicates the position data are overspecified. Inthis instance, the large lattice position data should beredefined and the job rerun.

3 - 7

Figure 3-1Typical Job Deck

REGTEST,BXXXX-YYYYY,T40,IO40.ATTACH ,MICRETE ,MICRETE41, ID»^ tDD.MICRETE.7/8/9 END-OP-RECORDSELECTREGULAR

DEFINEZED-2 CANDU LATTICE SIMULATIONLEVEL COEFFICIENT OF REACTIVITY CALCDLATION

1.0

1 .0 .

1 CAND'J

055

EXECUTEEND7/8/96/7/8/9

60.02.0

2529391670

5.231.0

0 1 1O i l1 1 2

22.01.0

1.054240.91670

1.545

0 11 12 1

END-OF-RECORDEND-OF-FILE

1 .

223

i i3364

11181

012

2.01.0

.41

.00

0 .

111

87908

334

224.7360010.0

138.3023,

138.

0

2

.95

.00

.95

1

1

138

4

3

168.1.0

.0

7485.0200.0

. 95

0

3

144

1

1

Figure 3-2Output from Typical Job

RUN DATE - 82-05-15

MICRETE - VERSION 4.1(1982 MAX 15)

USER INPUT

RUN TIME - 16.27.55.

CARDNUMBER

• • • • • .

00001000020000300004000050000600007000080000900010000110001200013000140001500016000170001800019000200002100022

1 10.V VSELECT

REGULAR

DEFINE

20. . V . .

ZED-2 CANDU LATTICELEVEL COEFFICIENT OF

1.060.0

2.0

1.252930.91670

1 CANDU 5

0 0 15 0 15 1 1

EXECUTEEND

.231.0

112

30V . .

SIMULATION

CARD IMAGE40

. . . V . . • • • • •

REACTIVITY CALCULATION

22.01.0

1.054240.91670

1.545

0 11 12 1

113364

1 . 1 1 1 8 1

2 02 13 2

2.01.0

.41

.00

50. .V. .

60V..

224.73600

0.87908

111

334

10.0

138.953023.00

138.95

0 11 12 1

70V

168.01.0

7485.0200.0

138.95 144.

4 0 14 1 13 3 1

CARDNUMBER

80. . . V . .

00001000020000300004000050000600007000080000900010000110001200013

.21 000140001500016000170001800019000200002100022

3 - 8

Figure 3-2 (cont'd)Output from Typical Job

MICRETE •> VERSION 4.1(1982 MAY IS)

REGULAR

RUN DATE - 82-05-15

MICRETE

RON TIME - 16.28.00.

PROGRAM SIZE DATA

NUMBER OF RODS IN SECTOR OF SYMMETRYNUMBER OF UNIQUE ROD TYPESNUMBER OF RODSNUMBER OF VESSEL FUNCTION EVALUATIONS

IS ( 98 MAX)1 ( 20 MAX)

121 ( 7S0 MAX)44 ( 1200 MAX)

DESCRIPTIVE TITLE — VOLUME 0

ZED-2 CANDU LATTICE SIMULATIONLEVEL COEFFICIENT OF REACTIVITY CALCULATION

LATTICE DESCRIPTION AND CALCULATION CONTROL DATA — VOLUME 1

LATTICE DATA — RECORD 1

INTERSTITIAL FACTOR FOR TYPICAL ROD, TRYYSURFACE FLUX CALCULATION SWITCH (1-ON), SURFROD POWER CALCULATION SWITCH (1=ON), PPOW

GEOMETRIC DATA — RECORD 2

LATTICE ARRANGEMENT, LATARNG = 50 DEGLATTICE SPACING, LAM = 22.00000 CMSYMMETRY, SP = 2EXTRAPOLATED HEIGHT, H = 224.73600 CMCORE RADIUS, RCOR = 168.00000 CMREFLECTOR OUTER RADIUS, RP = 200.00000 CM

ITERATION CONTROL DATA — RECORD 3

ITERATION PARAMETER, PARAMTYPE NUMBER OF TYPE <ITER> ROD, ITERINITIAL ESTIMATE OF KEFF, EKEFFITERATION PARAMETER INITIAL INCREMENT, INCLEVEL COEFFICIENT OP REACTIVITY CALCULATIONSWITCH (0»OFF), LCRIND

MODERATOR PROPERTIES — RECORD 4

FAST DIFFUSION COEFFICIENT, DF » 1.2529THERMAL DIFFUSION COEFFICIENT, D * 1.0542SLOWING DOWN AREA, LSSQM - 113.41TYPICAL CELL SLOWING DOWN AREA, LSSQC - 138.95MODERATOR DIFFUSION AREA, LSQM • 7485.0

1.000000.000000.00000

21

1.0000010.00000

CMCMCM**2CM** 2CM** 2

REFLECTOR PROPERTIES — RECORD 5

FAST DIFFUSION COEFFICIENT, DFRTHERMAL DIFFUSION COEFFICIENT, DRSLOHINp DOWN AREA, LSSQRDIFFUSION AREA, LSQROUTER RADIUS OF INNER REFLECTOR, RP

.91670 CM

.91670 CM364.00000 CM**23023.00000 CM**2200.00000 CM

REFLECTOR OUTER BOUNDARY CONDITIONS AND BUCKLING CALCULATION CONTROL DATA — RECORD 6

FAST FLUX BOUNDARY CONDITION, ALPHAF « O.OCOOO(1-PERFBCT PEfLECTOR, 0-BLACK BOUNDARY)THERMAL FLUX BOUNDARY CONDITION, ALPHA - 0.00000FIRST BUCKLING POINT COORDINATE, IPX - 0SECOND BUCKLING POINT COORDINATE, IP2 - . 0THIRD BUCKLING POINT COORDINATE, IP3 • 0

3 - 9


ROD AND CELL PROPERTY DATA — VOLUME 2

TY - TYPE NOMBERRODID - IDENTIFIERRODRAD - RADIUS, CMGNOT - RATIO OF SURFACE TO AVERAGE THERMAL FLUXKINF - K-INFINITYPP - RESONANCE ESCAPE PROBABILITYLFCRSQ - RADIAL SLOWING DOWN AREA, CM**2LFCASQ - AXIAL SLOWING DOWN AREA, CM**2LSQ - DIFFUSION AREA, CM**2F - ROD INTERSTITIAL FACTORFROD - ROD THERMAL UTILIZATION FACTORFF - FUEL THERMAL UTILIZATION FACTOR (USED ONLY

POWERS ARE COMPUTED)FN - FUEL POWER FACTOR IN POWER / THERMAL NEUTRON

ABSORBED (USED ONLY WHEN POWERS ARE COMPUTED)

REC

1

I RODID

1 CANDU

RODRAD GNOTFROD

5.23000 1 . 5 4 5 0 01.00000 0 . 0 0 0 0 0

FKINF

FF1,1118)

O.OjOOO

PP LFCHSQ LFCASQ LSQFN

.87908 138.95000 138.95000 144.210000.00000

ROD POSITION DATA — VOLUME 3

REC - RECORD NUMBER -P - POSITION COORDINATEQ - POSITION ORDINATETY - ROD TYPE

REC16

11

P0.5.5.

Q0 .0 .1 .

TY1 .1 .1 .

P1.1.2 .

Q0 .1 .2 .

TY1 .1 .1 .

P2 .2 .3 .

Q0 .1 .2 .

TY1 .1 .1 .

P3 .3 .4 .

Q0.1.2.

TY1.1.1.

P4 .4 .3 .

Q TY0 . 1 .1 . 1 .3 . 1 .

1015

LATTICE MAP CONSISTING OF 121 RODS

P-AXIS » >-10

I . . .

Q

A '.XI -5>S

v !VV 0>

5>

- 5I

1 1 1 1 11 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1l l l l l l l l l ' l

1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1

1 1 1 1 1

10I

< - 1 0

< - 5

< 5

10 >I

- 1 0I

10

10

3 - 1 0


MICRETE PROBLEM SOLUTION

RESULTS — INTERMEDIATE CALCULATIONS

DET HEIGHT

.478B4958E-12 234.73600-.56931004E-14 221.36593.26396322E-15 221.52302.13648723E-1B 221.51606

-.394665UE-23 221.51605

RESULT? — FINAL

HEIGHT ' 221.51605

COMPUTED PROPERTIES

NO

123456789

101112131415

p

0.1.2.3.4.5.1.2.3.4.5.2.3.4.3.

g

0.0.0.0.0.0.l.l.I.I.l.2.2.2.3.

TY

111111111111111

1111111111

11

1

RHO

.92604

.88359

.75908

.56084

.30357

.03735

.80011

.63868

.41046

.13715

.90874

.44708

.20113

.97029

.00000

22211̂

12

PHI

.26787

.21789

.07126

.83763

.53065

.12481

.119581.9294211

11

1

.65946

.31916

.83669

.70289

.40079

.97125

.00325

777654765435444

All

.94810

.77295

.25911

.44107

.37938

.28080

.42843

.76227

.82048

.69262

.75005

.97160

.95666

.00406

.12666

CII

.14819

.14819

.14819

.14817

.14778

.13647

.14819

.14819

.14807

.14600

.1158B

.14810

.14677

.12598

.12627

RADIUS

0224466881103858791001227695116114

.00000

.00000

.00000

.0C000

.00000

.00000

.10512

.20653

.32213

.81667

.49082

.21024

.89578

.41306

.31535

NO - ROD NUMBER RADIUS - DISTANCE TO LATTICE CENTRE, CMRHO - RELATIVE THERMAL FLUX PHI - RELATIVE PAST FLUXAll - RELATIVE THERMAL ABSORPTIONS/UNIT LENGTH CII - RATIO OF RESONANCE TO THERMAL ABSORPTIONS

SUM OF SQUARES OF THERMAL FLUX - .3107S702E+02SUM OF FAST TIMES THERMAL FLUX - .35889072E+02

B»*2 « 3.84336 M** (-2) (JO FIT TO FLUX AT POSITIONS (P,Q) = ( 0, (,) AND ( 3, 0) )

B**2 • 3.84261 M**(-2) (J0+I0 FIT TO FLUX AT POSITIONS (P,Q) » ( 0, 0) AND ( 1, 0) AND ( 3, 01

MATERIAL BUCKLING FROM TWO-GROUP CELL PARAMETERS - 3.84408 M*«(-2)

K-INFIN1TV CALCULATED FROM MICRETE BUCKLING AND TWO-GROUP CELL PARAMETERS - 1.1117884

LEVEL COEFFICIENT OF REACTIVITY CALCULATION

DET EIGENVALUE

.37772291E-13 I.OOOLOOO-.55138690E-16 .99947011.80039485E-19 .99947088

.75284997E-13 1.0000000-.21940514E-15 ."9894585.63230819E-18 .99894890

-.38033408E-13 1.0000000-.55714712E-16 1.000S356-.82077218E-19 1.0005364

-.76329457E-13 1.0000000-.22401303E-15 1.0010770-.66491373E-18 1.0010802

LEVEL COEFFICIENT OF REACTIVITY - .53279 MK/CMEFFECTIVE (M«2) *F (H)/ICIHF » 293.38500 CM*«2

>» MICRETE EXECUTION COMPLETE - ALL USER INPUT WAS PROCESSED <<<

3 - 1 1

Figure 3-3Substitution Experiment Analysis Job Deck

SUBTEST,BXXXX-YYYYY,T40,1040.ATTACH,MICRETE,MICRETE41,ID'JUDD.M1CRETE.7/8/9 END-OF-RECORDSELECT

SOBSTITOTION

DEFINEDETERMINATION OF LATTICE PARAMETERS OSING FEW RODSCANDO FUEL

10

1.60.2.

10.

.0,00,0

.25293

.91670

1 CANDU

2 19 UO2

3 7 002

4 19 U

5 ZEEP

0eD5

EXECUTE

0

u1

SOBSTITOTE19 002

6

EXECUTEEND7/8/96/7/8/9

FUEL1133

0

1

l

3.

5.231.0

5.231.0

4.221.0

4.451.0

1.751.0

11X

2

WITH HB40

1

2312

6

.6500022.01.0

10.01.054240.91670

1.545

1.574

1.525

1.812

1.964

0 11 1J. J.

2 1

ORGANIC4201

1 1

END-OF-RECORDEND-OF-FILE

113364

1 11181

1.03865

1.13859.

1.10068

1.24294

2 0

3 2

COOLANT237.954

2.00

5 2

2.01.0

.41

.00

0.87908

0.39504

0.88386

0.84634

0.95059

1 3

1 4

2.2.

1 4

1.0224.73600

10.0

1383023

138

115

143

141

115

0

2

3

.95

.00

.95

.27

.56

.91

.7U

1

1

1

138

115

143

141

115

4

3

3

168.00,.001

7485.0:

.95

.27

.56

.91

.70

0

3

4

200.0

144

132

147

105

279

1

1

1

.21

.14

.71

.80

.39

3 - 1 2

Figure 3-4Output from Substitution Experiment Analysis Job

a) Reference lattice calculation

SUBSTITUTION MICRETE

RUN DATE - 82-05-15

PROGRAM SIZE DATA

MICRETE - VERSION 4.1(1982 MAY 15)

REFERENCE LATTICE CALCULATION

RUN TIME - 16.26.59.

NUMBER OF RODS IN SECTOR OP SYMMETRYNUMBER OF UNIQUE ROD TYPESNUMBER OF RODSNUMBER OF BESSEL FUNCTION EVALUATIONS

15 ( 98 MAX)5 ( 20 MAX)

121 ( 750 MAX)44 ( 1200 MAX)


DETERMINATION OF LATTICE PARAMETERS USING FEW RODS (AECL-2C93)CANDU FUEL

LATTICE DESCRIPTION AND CALCULATION CONTROL DATA — VOLUME 1


INTERSTITIAL FACTOR FOR TYPICAL ROD, TRYYREFERENCE LATTICE BUCKLING, BCEALTERNATE SLOWING DOWN SOURCE (1=OHITTED), BAASURFACE FLUX CALCULATION SWITCH (1=ON), SURF


LATTICE ARRANGEMENT, LATT.RNG = 60 DEGLATTICE SPACING, LAM = 22.00000 CMSYMMETRY, SP = 2EXTRAPOLATED HEIGHT, H = 224.73600 CMCORE RADIUS, RCOR = 168.00000 CMREFLECTOR OUTER RADIUS, RP = 200.00000 CM


ITERATION PARAMETER, PARAMTYPE NUMBER OF TYPE <ITER> ROD, ITERINITIAL ESTIMATE OF KEFF, EKEPFITERATION PARAMETER INCREMENT, INCITERATION PARAMETER INCREMENT SUBSTITUTED LATTICE, INCSITERATION PARAMETER INCREMENT SMALL TEST LATTICE, INCTITERATION PARAMETER'INCREMENT LARGE TEST LATTICE INCTL

1.000003.85000 M**(-2)Q.000001.00000

61

1.0000010.00000

.0010010.0000010.00000

CMCMCM**2CM** 2CM**2


FAST DIFFUSION COEFFICIENT, DF • 1.2529THERMAL DIFFUSION COEFFICIENT, D = 1.0542SLOWING DOWN AREA, LSSQM = 113.41TYPICAL CELL SLOWING DOWN ARE"., LSSQC • 138.95MODERATOR DIFFUSION AREA, LSQM = 7435.0

REFLECTOR PROPERTIES ~ RECORD 5

FAST DIFFUSION COEFFICIENT, DFR » .91670 CMTHERMAL DIFFUSION COEFFICIENT, DR » .91670 CMSLOWING DOWN AREA, LSSQR =• 364.00000 CM**2DIFFUSION AREA, LSQR » 3023.00000 CM**2OUTER RADIUS OF INNER REFLECTOR, RP = 200.00000 CM

REFLECTOR OUTER BOUNDARY CONDITIONS AND ttJCKLIUG CALCULATION CONTROL DATA — RECORD 6

FAST FLUX BOUNDARY CONDITION, ALPHAF • 0.00000(l'PERFECT REFLECTOR, 0-BLACK BOUNDARY)THERMAL FLUX BOUNDARY CONDITION, ALPHA • 0.00000FIRST BUCKLING POINT COORDINATE, IP1 - 0SECOND BUCKLING POINT COORDINATE, IP2 - 0

' THIRD BUCKLING POINT COORDINATE, IP3 > 0

3 - 1 3

Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job



TY - TYPE NUMBERRODID - IDENTIFIERRODRAD - RADIUS, CMGNOT - RATIO OP SURFACE TO AVERAGE THERMAL FLUXKIHF - K-INFINITYPP - RESONANCE ESCAPE PROBABILITYLFCRSQ - RADIAL SLOWING DOKN AREA, CM**2LFCASQ - AXIAL SLOWING DOWN AREA, CM**2LSQ - DIFFUSION AREA, CM**2F - ROD INTERSTITIAL FACTORFROD - ROD THERMAL UTILIZATION FACTORFF - FUEL THERMAL UTILIZATION FACTOR (USED ONLY

POWERS ARE COMPUTED)FN - FUEL POWER FACTOR IN POWER / THERMAL 'NEUTRON


REC

1

2

3

4

5

I

).

2

3

4

5

DD POSITION

RODID

CANDU

19 UO2

7 UO2

19 U

ZEEP

DATA —

RODRADF5.23000

1.000005.230001.000004.22000

1.000004.450001.000001.750001.00000

VOLUME 3

GNOTFROD1.54500

0.000001.57400

0.000001.52500

0.000001.81200

0.000001.96400

0.00000

KINFFF1.11181

0.000001.03865

0.000001.13859

0.000001.10068

0.000001.24294

0.00000

PPFN

0

0

0

0

0

.87908.00000.89504

.00000.88386

.00000.84634

.00000.95059

.00000

LFCRSQ

138.

115.

143.

141.

115.

95000

27G00

56000

91000

70000

LFCASQ

138.

115.

143.

141.

115.

95000

27000

56000

91000

70000

LSQ

144.

132.

147.

105.

279.

21000

14000

71000

80000

39000

REC - RECORD NUMBERP - POSITION COORDINATEQ - POSITION ORDINATETY - ROD Ty?E

REC P1 0.6 5.j.1 5.

Q0.0.1.

TY1.1.1.

P1.1.2.

Q0.1.2.

TY1.1.1.

P2.2.3.

Q0.1.2.

TY1.1.1.

P3.3.4.

Q0.1.2.

TY1.1.1.

P4.4.3.

Q0.1.3.

TY REC1. 51. 101. 15


-10I

P-AXIS » >-5

I10I

AXI -5>S

VVV 0>

1 1 1 1 11 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1

1 1 1 1 1< 5

I-10

I10

3 - 1 4



HICRETE PROBLEM SOLUTION

RESULTS --' INTERMEDIATE CALCULATIONS

DEI REF. RAD.

.19712755E-12

.94483765E-13

.37500121E-13

.47122830E-14

.28394211E-15

.19841979E-17

.82766219E-21

210.00000184.20751192.56443190.19001189.84875189.8681.)189.86801

B**2 - 3.84418 M**(-2) (JO PIT TO FLUX AT POflTIONS (P,Q)

DET REF. RAD.

.13022739E-12

.28317940E-14

.70840763E-15

.28441172E-17

.28722856E-20

199.86815188.95014189.18250189.13600189.13582

B**2 - 3.85005 M**(-2) (JO FIT TO FLUX AT POSITIONS (P,Q)

RESULTS — FINAL

REF. RAD. - 189.13582

0, 0) AND ( 3, 0) )

( 0, 0) AND ( 3, 0) )

COMPUTED PROPERTIES

NO

123456789101112131415

P

0.1.2.3.4.5.1.2.3.4.5.2.3.4.3.

Q

0.0.0.0.0.0.1.1.1.1.1.2.2.2.3«

TY

111111111111111

111111111^

11

1

RHO

.99193

.94651

.81339

.60177

.32764

.04184

.85724

.68482

.44151

.15031

. :ooi5

.48054

.21858

.96824

.00000

2221112111

11

1

PHI

.34520

.29173

.13499

.88562

.5S895

.13276

.18662

.98354

.69588

.33518

.83546

.74213

.42151

.97446

.00834

8.8.7.6.5.4.7.6.5.4.3.6.5.3.4.

All

219610322148288609644784429912663839523494832746717144210938028429953912646

CII

.14802

.14802

.14801

.14800

.14762

.13669

.14802

.14801

.14790

.14592

.11668

.14793

.14666

.12653

.12677

RADIUS

0224466881103858791001227695116114

.00000

.00000

.00000

.00000

.ooooo.00000

.10512

.20653

.32213

.81667

.49082

.21024

.89578

.41306

.31535

222111221111111

RHOSF

.46837

.41209

.24712

.98489

.64518

.29092

.30146

.08780

.78629

.42542

.11517

.83466

.51003

.19962

.23898

222111211^

11

PHIS

.34188

.28848

.13196

.88293

.55650

.12" -

.18352

.98072

.69339

.33214

.82093

.73960

.41871

.95323

.99686

NO - ROD NUMBERRHO - RELATIVE THERMAL FLUXAll - RELATIVE THERMAL ABSORPTIONS/UNIT LENGTHRHOSF - RELATIVE THERMAL FLUX ON CELL SURFACE

RADIUS - DISTANCE TO LATTICE CENTRE, CMPHI - RELATIVE FAST FLUXCII - RATIO OF RESONANCE TO THERMAL ABSORPTIONSPHISF - RELATIVE FAST FLUX ON CELL SURFACE

B**2 - 3.85005 M**(-2)

B " 2 - 3.84901 M**(-2)

(JO FIT TO FLUX AT POSITIONS (P,Q) - (

(J0+I0 FIT TO FLUX AT POSITIONS (P,Q)

0, 0) AND ( 3, 0) )

( 0, 0) AND ( 1, 0) AND ( 3, 0)

3 - 1 5


b) Substituted lattice calculation++•++++++++++++++++++++++++++++++ HICRETE - VERSION 4.1 ++ (1982 MAY 15) +


RUN DATE - 82-05-15

SUBSTITUTED LATTICE CALCULATION

RUN TIME - 16.27.26.

PROGRAM SIZE DATA

NUMBER OP RODS IN SECTOR OF SYMMETRYNUMBER OF UNIQUE ROD TYPESNUMBER OF RODSHUMBER OF BESSEL FUNCTION EVALUATIONS

15 ( 98 MAX)5 ( 20 MAX)

121 ( 750 MAX)44 ( 1200 MAX)


DETERMINATION OF LATTICE PARAMETERS USING FEW RODS (AECL-2593)19 UO2 FUEL WITH HB40 ORGANIC COOLANT

LATTICE DESCRIPTION AND CALCULATION CONTROL DATA -- VOLUME 1


INTERSTITIAL FACTOR FOR TYPICAL ROD, TKYYREFERENCE LATTICE BUCKLING, BCE =ALTERNATE SLOWING DOWN SOURCE (1-OMITTED), BAA =SURFACE FLUX CALCULATION SWITCH (1»ON), SURF =


LATTICE ARRANGEMENT, LATARNG = 60 DEGLATTICE SPACING, LAM " 22.00000 CMSYMMETRY, SP = 2EXTRAPOLATED HEIGHT, H • 237.95400 CMCORE RADIUS, RCOR = 168.00000 CMREFLECTOR OUTER RADIUS, RP » 1B9.13582 CM


ITERATION PARAMETER, PARAMTYPE NUMBER OF TYPE <ITER> ROD, ITERINITIAL ESTIMATE OF KEFF, EKEFFITERATION PARAMETER INCREMENT, INCITERATION PARAMETER INCREMENT SUBSTITUTED LATTICE,ITERATION PARAMETER INCREMENT SMALL TEST LATTICE,

1.000003.85000 M**(-2)0.000001.00000

INCSINCT

ITERATION PARAMETER INCREMENT LARGE TEST LATTICE, INCTL

32

1.00000.00100.00)00

10.0000010.00000


FAST DIFFUSION COEFFICIENT, DFTHERMAL DIFFUSION COEFFICIENT, DSLOWING DOWN AREA, LSSQMTYPICAL CELL SLOWING DOWN AREA, LSSOCMODERATOR DIFFUSION AREA, LSQM


FAST DIFFUSION COEFFICIENT, DFRTHERMAL DIFFUSION COEFFICIENT, DRSLOWING DOWN AREA, LSSQRDIFFUSION AREA, LSQROUTER RADIUS OF INNER REFLECTOR, RP

1.25291.0S42113.4113B.957485.0

CMCMCM** 2CM**2CM** 2

.91670 CM

.91670 CM364.00000 CM**23023.00000 CM**2189.13582 CM


FAST FLUX BOUNDARY CDNDITION, ALPHAF - 0.00000U-PERFECT REFLECTOw 0-8LACK BOUNDARY)THERMAL FLUX BOUNDARY CONDITION, ALPHA - 0.00000FIRST BUCKLING POINT COORDINATE, IP1 - 0SECOND BUCKLING POINT COORDINATE, IP2 - 3THIRD BUCKLING POINT COORDINATE, IP3 - 3

3 - 1 6


b) Substituted lattice calculation


TY - TYPE NUMBERRODID - IDENTIFIERRODRAD - RADIUS, CMGNOT - RATIO OP SURFACE TO AVERAGE THERMAL FLUXKINF - K-INFINITYPP - RESONANCE ESCAPE PROBABILITYLFCRSQ - RADIAL SLOWING DOWN AREA, CM"*2LFCASQ - AXIAL SLOWING DOWN AREA, CM**2LSQ - DIFFUSION AREA, CM**2F - ROD INTERSTITIAL FACTORFROD - ROD THERMAL UTILIZATION FACTORFF - FUEL THERMAL UTILIZATION FACTOR (USED ONLY

POWERS ARE COMPUTED)FN - FUEL POWER FACTOR IN POWER / THERMAL .NEUTRON


REC

1

2

3

4

5

RODID

CANDU

19 U02

7 UO2

19 U

ZEEP

RODRADF5.23000

1.000005.23000

1.000004.22000

1.000004.45000

1.000001.75000

1.00000

GNOTFROD1.54500

0.000001.57400

0.000001.52500

0.000001.81200

0.000001.96400

0.00000

ROD POSITION DATA — VOLUME 3

REC - RECORD NUMBERP - POSITION COORDINATE0 - POSITION ORDINATETY - ROD TYPE

REC16

11

P0.5.5.

Q0.0.1.

TY2.1.1.

P1.1.2.

Q0.1.2.

TY2.1.1.

KINFFF1.1119B

0.000001.03865

0.000001.13J59

0.000001.10068

0.000001.24294

0.00000

P2.2.3.

Q0.1.2.

PPFN

LFCRSQ LFCASQ LSQ

.87922 138.95000 138.95000 144.210000.00000

.89504 115.27000 115.27000 132.140000.00000

.88386 143.56000 143.56000 147.710000.00000

.84634 141.91000 141.91000 105.800000.00000

.95059 115.70000 115.70000 279.390000.00000

TY1.1.1.

P3.3.4.

Q0.1.2.

TY1.1.1.

P4.4.3.

Q0.1.3.

TY REC1. 51. 101. 15

LATTICE MAP CONSISTING OP 121 RODS

-10I

P-AXIS » >-5I

10I

AXI -5>S

VVV 0>

1 1 1 1 1 .1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 2 2 1 1 1 1 11 1 1 1 2 2 2 1 1 1 11 1 1 1 1 2 2 1 1 1 1 . 11 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1

1 1 1 1 1

< -5

< 0

< 5

I-10

I10

10

3 - 1 7


b) Substituted lattice calculation



DET

.74971425E-14

.90430643E-17

.47977466E-20

.89604000

.89681776

.89681870

RESULTS — FINAL

P * .89681870

COMPUTED PROPERTIES

NO

123456

89101112131415

P

0.1.2.3.4.5.

2.3.4.5.2.3.4.3.

Q

0.0.0.0.0.0.

1.1.1.1.2.2.2.3.

TY

221111

11111111

111111

111

11

1.

RHO

.81592

.79019

.69597

.54032

.30459

.03932• 1 £D\) I

.60453

.40581

.14091

.90376

.43955

.20457

.96925

.00000

1.1.1.1.1.1.•1

X •

1.1.1.

1.1..

1.

PHI

.81746,8566196708,81225.5318112884Q7fl VC

8858365377323948370969372404929738200656

886654•J1

65435434

All

1.27432.15705.99834.35606.38334.288711 1 AA5* 11943.62102.30100.70792.72932.94023.97060.99959.12646

CII

.09734

.10087

.14582

.14791

.14762

.136551 £41 ft

• 1441D

.14776

.14789

.14589

.11644L4792.14663.12631.12654

RADIUS

P22446688110

JO58791001227695116114

00000.00000.00000.00000.00000.000001 nci o

. 1U Jl^

.20653

.32213

.81667

.49082

.21024

.89578

.41306

.31535

222111

11111111

RHOSF

.25883

.22688

.10133

.90850

.61643

.287641 ̂ 71fi

.LJ/JO

.98806

.74184

.41360

.11951

.78365

.49249

.20073

.23882

1111111J.

111

11

PHIS

.81897

.86186

.96219

.80931

.52913

.12140QTOOQ

• 7 /£U?

.88265

.65106

.32069

.82225

.69096

.40190

.96231

.99480


RADIUS - DISTANCE TO LATTICE CENTRE, CMPHI - RELATIVE FAST FLUXCII - RATIO OF RESONANCE TO THERMAL ABSORPTIONSPHISF - RELATIVE FAST FLUX ON CELL SURFACE

3 - 1 8


c) Test lattice calculation

HICRETE - VERSION 4.1(1982 MAY 15)


RUN DATE - 8 2 - 0 5 - 1 5++++•+++ (•++++++++++++++++++++++++++

TEST LATTICE CALCULATION - SMALL CORE

RUN TIME - 1 6 . 2 7 . 3 2 .

PROGRAM SIZE DATA

NUMBER. OF RODS IN SECTOR OP SYMMETRYNUMBER OP UNIQUE ROD TYPESNUMBER OP RODSNUMBER OP BESSEL FUNCTION EVALUATIONS

IS ( 98 MAX)5 ( 20 MAX)

121 ( 750 MAX)44 ( 1200 MAX)


DETERMINATION OF LATTICE PARAMETERS USING PEW RODS (AECL-2593)19 UO2 FUEL WITH HB40 ORGANIC COOLANT

LATTICE DESCRIPTION AMD CALCULATION CONTROL DATA — VOLUME 1

LATTICE DATA -- RECORD 1

INTERSTITIAL FACTOR FOR TYPICAL ROD, TRYY =•REFERENCE LATTICE BUCKLING, BCEALTERNATE SLOWING DOWN SOURCE (1-OMITTED), BAA =SURFACE FLUX CALCULATION SWITCH (1-ON), SURF

1.000003.85000 M**C-2)0.000001.00000

GEOMETRIC DAT.". — RECORD 2

LATTICE ARRANGEMENT, LATARNGLATTICE SPACING, LAMSYMMETRY, SPEXTRAPOLATED HEIGHT, HCORE RADIUS, RCORREFLfiCTOR OUTER RADIUS, RP

60 DEG22.00000 CM

2237.95400 CM168.00000 CM189.13582 CM


ITERATION PARAMETER, PARAMTYPE NUMBER OF TYPE <ITER> ROD, ITERINITIAL ESTIMATE OF KEPF, EKEFFITERATION PARAMETER INCREMENT, INCITERATION PARAMETER INCREMENT SUBSTITUTED LATTICE, INCSITERATION PARAMETER INCREMENT SMALL TEST LATTICE, INCTITERATION PARAMETER INCREMENT LARGE TEST LATTICE, INCTL


22

1.0000010.00000

.0010010.0000010.00000

FAST DIFFUSION COEFFICIENT, DFTHERMAL DIFFUSION COEFFICIENT, DSLOWING DOWN AREA, LSSQMTYPICAL CELL SLOWING DOWN AREA, LSSQCMODERATOR DIFFUSION AREA, LSQH

REFLECTOR PROPERTIES — RECORD S

FAST DIFFUSION COEFFICIENT, DFRTHERMAL DIFFUSION COEFFICIENT, DRSLOWING DOWN AREA, LSSQRDIFFUSION AREA, LSQROUTER RADIUS OF INNER REFLECTOR, RP

1.25291.0542113.41138.957485.0

CMCMCM** 2CM** 2CM** 2

.91670 CM

.91670 CM364.00000 CM**2

3023.00000 CM**2139.13582 CM


FAST FLUX BOUNDARY CONDITION, ALPHAF • 0.00000(1-PERFECT REF'"TOR, 0-BLACK BOUNDARY)THERMAL FLUX BOUNDARY CONDITION, ALPHA - 0.00000FIRST BUCKLING POINT COORDINATE, IP] - 0SECOND BUCKLING POINT COORDINATE, IP.' - 3THIRD BUCKLING POINT COORDINATE, IP. - 3

f

3 - 1 9



ROD AND CELL PROPERTY DMA — VOLUME 2

TY - TYPE NUMBERRODID - IDENTIFIERRODRAD - RADIUS/ CMGNOT - RATIO OF SURFACE TO AVERAGE THERMAL FLUXKINF - K-INFINITYPP - RESONANCE ESCAPE PROBABILITYLFCRSQ - RADIAL SLOWING DOWN AREA, CM**2LFCASQ - AXIAL SLOWING DOWN AREA, CM**2LSQ - DIFFUSION AREA, CM**2F - ROD INTERSTITIAL FACTORFROD - ROD THERMAL UTILIZATION FACTORFF - FUEL THERMAL UTILIZATION FACTOR (USED ONLY

POWERS ARE COMPUTED]FN - FUEL POWER FACTOR IN POWER / THERMAL NEUTRON


REC

1

2

3

4

5

I

1

2

3

4

5

ROD POSITION

RODID

CANDU

19 UO2

7 UO2

19 U

ZEEP

DATA —

RODRADF5.230001.000005.230001.000004.220001.000004.450001.000001.750001.00000

VOLUME 3

GNOTFROD1.545000.000001.57400

0.000001.525000.000001.812000.000001.96400

0.00000

KINFFF1.11198

0.000001.04071

0.000001.13859

0.000001.100680.000001.242940.00000

LFCRSQ LFCASQ LSQPPFN

.87922 138.95000 138.95000 144.210000.00000

.89682 115.27000 115.27000 132.140000.00000

.88386 143.56000 143.S6000 147.710000.00000

.84634 141.91000 141.91000 105.800000.00000

.95059 115.70000 115.70000 279.390000.00000

REC - RECORD NUMBERP - POSITION COORDINATEQ - POSITION ORDINATETY - ROD TYPE

REC P1 0.6 5.11 5.

Q0.0.1.

TY2.2.2.

P1.1.2.

Q0.1.2.

TY2.2.2.

P2.2.3.

Q0.1.2.

TY2.2.2.

P3.3.4.

Q0.1.2.

TY2.2.2.

t4.4.3.

Q TY REC0. 2. 51. 2. 1"3. 2. 15


P-AXIS » >-10I

Q

AXI -5>S

V '.V

v o>

-5I

2 2 2 2 22 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 22 2 2 2 2 ? 2 2

2 2 2 2 2

10I

< -10

< -5

< 0

II

-10I10

10

3 - 2 0




RESULTS -- INTERMEDIATE CALCULATIONS

DET HEIGHT

-.444682708-11 247.95400-.20254300E-U 455.06474-.13335925E-11 628.16403-.84308874E-12 961.83182-.60696329E-12 1535.3475

????????? MICRETE WASHING ERROR NUMBER - 2.05 - SHALL CORE CALCULATION FAILED

J???????? MICRETE WARNING ERROR NUMBER - 207 - CHECK CONSISTENCY OF POSITION AND SYMMETRY DATA

3-21


c) Test Iattic3 calculation

MICRETE - VERSION 4.1(1982 MAY 15)

SUBSTITUTION MICRETE TEST LATTICE CALCULATION - LARGE CORE

RUN DATE - 82-05-15 RUN TIME - 16.29.37.

PROGRAM SIZE DATA

NUMBER OF RODS IN SECTOR OF SYMMETRYNUMBER OF UNIQUE ROD TYPESNUMBER OF RODSNUMBER OF BESSEL FUNCTION EVALUATIONS

20 ( 98 MAX)5 ( 20 MAX)

163 ( 750 MAX)58 ( 1200 MAX)

DESCRIPTIVE TITLE — VOLDME 0

DETERMINATION OF LATTICE PARAMETERS USING FEW RODS (AECL-2593)19 UO2 FUEL WITH HB40 ORGANIC COOLANT

LA1TICE DESCRIPTION AND CALCULATION CONTROL DATA — VOLUME 1


INTERSTITIAL FACTOR FOR TYPICAL ROD, TRYYREFERENCE LATTICE BUCKLING, BCEALTERNATE SLOWING DOWN SOURCE (1-OMITTED), BAASURFACE FLUX CALCULATION SWITCH <1=ON), SURF

GEOMETRIC DATA ~ RECORD 2

LATTICE ARRANGEMENT, LATARNG = 60 DEGLATTICE SPACING, LAM ' 22.00000 CMSYMMETRY, SP = - 2EXTRAPOLATED HEIGHT, H = 237.95400 CMCORE RADIUS, RCOR - 168.00000 CMREFLECTOR OUTER RADIUS, RP = 189.13582 CM

ITERATION CONTROL DATA ~ RECORD 3

ITERATION PARAMETER, PARAMTYPE NUMBER OF TYPE <ITER> ROD, ITERINITIAL ESTIMATE OF KEFF, EKEFFITERATION PARAMETER INCREMENT, INCITERATION PARAMETER INCREMENT SUBSTITUTED LATTICE, INCSITERATION PARAMETER INCREMENT SMALL TEST LATTICE, INCTITERATION PARAMETER INCREMENT LARGE TEST LATTICE, INCTL

1.000003.85000 M*»(-2)0.000001.00000

22

1.0000010.00000

.0010010.0000010.00000


FAST DIFFUSION COEFFICIENT, DFTHERMAL DIFFUSION COEFFICIENT, DSLOWING DOWN AREA, LSSQMTYPICAL CELL SLOWING DOWN AREA, LSSQCMODERATOR DIFFUSION AREA, LSQM


FAST DIFFUSION COEFFICIENT, DFRTHERMAL DIFFUSION COEFFICIENT, DRSLOWING DOWN AREA, LSSO.RDIFFUSION AREA, LSQROUTER RADIUS OF INNER REFLECTOR, RP

1.25291.0542113.41138.957485.0

CMCMCM** 2CM** 2CM**2

.91670 CM

.91670 CM364.00000 CM**2

3023.00000 CH**2189.13582 CM


FAST FLUX BOUNDARY CONDITION, ALPHAF - 0.00000(1-PERFECT REFLECTOR, 0-BLACK BOUNDARY)THERMAL FLUX BOUNDARY CONDITION, ALPHA - 0.00000FIRST BUCKLING POINT COORDINATE, IP1 - 0SECOND BUCKLING POINT COORDINATE, IP2 - 3THIRD BUCKLING POINT COORDINATE, IP3 > 3

3 - 2 2




TY - TYPE NOMBERBODID - IDENTIFIERRODR'»D - RADIUS, CMGNOT - RATIO OF SURFACE TO AVERAGE THERMAL FLUXKINF - K-INFINITYPP - RESONANCE ESCAPE PROBABILITYLFCRSQ - RADIAL SLOWING DOWN AREA, CM**2LFCASQ - AXIAL SLOWING DOWN AREA, CM**2LSQ - DIFFUSION AREA, C M " 2F - ROD INTERSTITIAL FACTORFROD - ROD THERMAL UTILIZATION FACTORFF - FUEL THERMAL UTILIZATION FACTOR (USED ONLY

POWERS ARE COMPUTED)FN - FUEL POWER FACTOR IN POWER / THERMAL NEUTRON


REC

1

2

3

4

5

I

1

2

3

4

5

ROD POSITION

RODID

CANDU

19 UO2

7 UO2

19 U

ZEEP

DATA —

RODRADF5.230001.000005.23000

1.000004.220001.000004.450001.000001.75000

1.00000

VOLUME 3

GNOTFROD1.54500

0.000001.57400

0.000001.52500

0.000001.81200

0.000001.96400

0.00000

KINFFF1.11198

0.000001.04071

0.000001.13859

0.000001.10068

0.000001.24294

0.00000

PPFN

0

0

0

0

0

.87922.00000.89682

.00000.88386

.00000.84634

.00000.95059

.00000

LFCRSQ

138

115

143

141

115

.95000

.27000

.56000

.91000

.70000

LFCASQ

138.

115.

143.

141.

115.

95000

27000

56000

91000

70000

LSQ

144.

132.

147.

105.

279.

21000

14000

71000

80000

39000

REC - RECORD NUMBERP - POSITION COORDINATEQ - POSITION ORDINATETY - ROD TYPE

16

1116

0. 0.5. 0.5. 1.6. 0.

TY2.2.2.2.

0.1.2.1.

2.2.2.2.

2.2.3.5.

0.1.2.2.

TY2.2.2.2.

3.3.4.4.

0.1.2.3.

2.2.2.2.

4.4.3.3.

0.1.3.4.

TY REC5

101520


-10I

P-AXIS » >-5

I10I

0>

5>

2 2 2 2 2 22 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 1 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2

2 2 2 2 2 2

< 0

I-10

I-5

I10

3 - 2 3





DET HEIGHT

.8432B48SE-1S

.35362841E-15

.21164080E-15

.109932B0E-15

.58137546E-16

.28388055E-16

.12219607E-16

.41806871B-17

.91326682E-18

.88069723E-19

.20728567E-20

.4B322071E-23

.4S681771E-27

247.95400126.59908555.61603747.92329955.781831189.09251411.72611579.98561667.48991691.94801694.55831694.62121694.6214

RESULTS — FINAL

HEIGHT * 1694.6214

COMPUTED PROPERTIES

NO

1234567891011121314151617181920

P

0.1.2.3.4.5.1.2.3.4.52.3.4.3.6.6.5.4.3.

Q

0.0.0.0.0.0.1.1.1.1.1.2.2.2.3.0.1.2.3.4.

TY

2222222222222222

222

2.2.2.1.1.1.2.2.1.1.1.1.1.1.1.1.

r1.1.

RHO

.3787533251196499786469178354032413806444812044993915011852925746124961284030101483305936190000000000

2.2.2.1.1.1.2.2.1.1.1.1.1.1.1.

p

PHI

,35273,30700.1724695698673023354521086041S4792114817012173832565563522423258069301766926803538570585705

10.10.10.9.7.6.10.9.8.6.5.8.7.5.5.4.3.4.4.4.

All

.83887,62818,008400157470866169682129440t>68256528320424054442911747869390850726027479582265785565355653

CII

.09620

.09620

.09620

.09620

.09616

.09593

.09620

.09620

.09619

.09611

.09486

.09619

.09613

.09529

.09529'

.08956

.07814

.08348

.08336

.08336

RADIUS

0.22.44.66.88.

110.38.58.79.

100.122.76.95.

116.114.132.144.137.133.133.

,00000.00000000000000000000000001051220653322138166749082210248957841306315350000026365389968207882078

22222122211211111111

RHOSP

.95590

.89845

.72942

.45871

.10225

.68255

.78520

.56533

.25169

.86319

.42914

.30249

.95666

.55279

.59555

.25514

.03498

.16318

.24246

.24246

222111221111111

PHIS

.34990

.30422

.16985

.95462

.67099

.33364

.21420

.03939

.78995

.47984

.11946

.83035

.55442

.22208

.25586

.92506

.65949

.79547

.84837

.84837


RADIUS - DISTANCE TO LATTICE CENTRE, CMPHI - RELATIVE PAST FLUXCII - RATIO OF RESONANCE TO THERMAL ABSORPTIONSPHISF - RELATIVE FAST FLUX ON CELL SURFACE

B**2 - 1.64962 M**(-2) (JO FIT TO FLUX AT POSITIONS (P,Q) - ( 0, 0) AND ( 3, 0) )

B « 2 » 1.64854 M**(-2) (J0+I0 FIT TO FLUX AT POSITIONS (P,Q) - ( 0, 0) AND ( 1, 0) AND { 3, 0)

MATERIAL BUCKLING FROM TWO-GROUP CELL PARAMETERS > 1.62927 M**<-2)

K-INFINITY CALCULATED FROM MICRETE BUCKLING AND TWO-GROUP CELL PARAMETERS - 1.0412377

» > MICRETE EXECUTION COMPLETE - ALL USER INPUT HAS PROCESSED <<<

I

4 - 1

4. Model Equations and Associated Calculations

4.1 Model Equations and their Solution

The 'microscopic-discrete1 theory1*2 assumes that themoderator pervades the core and that fast and thermal neutronsobey their respective diffusion equations:

V2<f> - Kf$ + q f /D f = 0 4-1

V2p - KP + q/D = 0 4-2

where <p and p are the fast and thermal fluxes, K , D and qrepresent the diffusion area, the diffusion coefficient and thesource density, with the subscript 'f' denoting fast groupfactors. The model also assumes that equation source densitiesare proportional to the fast and thermal fluxes on the rod axes.By means of these sources each rod contributes to the fluxes onevery rod axis in a known analytical way (Reference 2) and thesum of the contributions to either flux on the rod axis mustequal that flux - this is the 'self-consistency' condition. Afull development of the governing equations is beyond the scopeof this document. For such a development the reader is referredto Reference 2. Suffice to say, application of this theory to areactor consisting an 'n1 rod lattice yields the following self-consistent matrix problem:

M - u[V][p] = 0 4-3

- 0 4-4

where [p] and [<J>] are 'n' element vectors, one element perrod, represerting thermal and fast fluxes on the rod axes. [U] ,[V], [W] and [Y] are nxn matrices of coupling coefficients, anda) is the problem eigenvalue which multiplies all terms

containing k-infinity.

The eigenvalue problem represented by equations 4-3 and 4-4is solved by multiplying equation 4-3 by [Y] and subtractingequation 4-4 from the resultant, producing:

[[W]-<o([Y][U]+[V])][p] = 0 4-5

which is solved by adjusting the eigenvalue, or relatedparameter such as extrapolated height until the determinant ofthe above equation is zero. Having determined the eigenvalue,relative thermal fluxes are computed by setting one of the rodthermal fluxes, [p], equation 4-5, to unity and by solving theresultant order n-1 matrix problem. Finally, rod fast fluxes

4 - 2

represented by [<(>] are computed directly using equation 4-3.

The reader is referred to Reference 2, page 19, for a detaileddefinition of the various elements of the coefficient matrices.

4.2 Buckling Calculations

A macroscopic parameter of prime importance is the buckling.If the lattice of interest consists entirely of one type of rod,MICRETE performs up to three buckling calculations: 1) a Jo

calculation, 2) a Jn+Io calculation and 3) a material bucklingcalculation.

The Jp-buckling is computed by summing the radial buckling,Aj , estimated by fitting the computed thermal flux to the one-group diffusion theory solution:

p(r) = A J0(Air) 4-6

at two points, and the axial buckling computed from theextrapolated height, H. Thus,

B̂ = [A? + ( £ )2] 4-7

Similarly, the Jg+I0-buckling* is computed by summing theradial buckling, Af, , estimated by fitting the computed thermalflux to the two-group diffusion theory solution:

P(r) = A JQ(A2r) + B IQ(gr) 4-8

at three points, and the axial buckling computed from theextrapolated height, H. Thus,

BJ +1 = &1 + < ft ̂ 4-9o o

Finally, the material buckling is estimated from the two-group criticality equation:

(1+K~2B2)(1+K"2B2)= 1 4-10

* - Serdula,K.S., 'Determination of Radial Buckling in ReflectedSystems', Nucl. Sci. Eng. 26, 1-12 (1966)

4 - 3

4.3 Surface Flux Calculations

It is sometimes useful for experimental analysis andcomparisons with other codes to calculate the rod surfacefluxes. Using Reference 2, equations 9-11, the rod fast fluxcan be represented by:

4>(r) = A1 4-11

Similarly, using equations 12, 13, 17, 18, 22 and 25 from thesame reference the rod thermal flux can be represented by:

p(r) = A1-(Df/D)

11-K7K *

K-2

(Kfr)]f

(Df/D)

1-K2/K2C2I0(Kfr)

(KP) + E' [ V'ur) -

- C 4-12

By setting r=0, relationships for C2 and C4 are derived fromequations 4-11 and 4-12, and the fast and thermal fluxes on therod surface at radius 'a' can be computed.

5 - 1

5. Program Description

MICRETE Version 4.1 is a FORTRAN V program, operational onthe CRNL CDC 6600/Cyber 170 computer system. It consists of 25subprograms, and uses approximately 143,0003 (51,00010) words ofcentral memory and 9 disk files to store intermediate and/orfinal results. Program structure is illustrated in Figure 5-1.

5.1 Subprogram Descriptions

MAIN, the MICRETE - Version 4.1 main program, directs MICRETEprocessing. First, it copies user input (TAPE5) to output(TAPE6). Then, in response to user input, it causes either'regular' or 'substitution' MLCRETE to execute.

ERRORS handles all MICRETE error processing. If user inputis in error the card associated with the error, its number and adiagnostic message are written to the output file, TAPE6.Otherwise, only an error diagnostic is written to TAPE6.

USERIN reads user input according to the MICRETE programdirectives; SELECT, DEFINE, MODIFY, SUBSTITUTE, RECALL, EXECUTEand END (Section 3.0).

EXX2 uses the half-interval method to compute an equivalentradius for a rod given the surface to centre thermal flux ratio(Reference 2, page 11).

IKBESS evaluates the Bessel functions Io, I±, KQ and K^ usingasymptotic expansions similar to those detailed in the Handbookof Mathematical Functions, edited by M.A. Abramowitz andI.A. Stegun.

PSM evaluates an (N-l) order power series in X, given its Ncoefficients.

GEOMTRY unfolds the lattice description according tospecified symmetry conditions. Hexagonal lattices having 0-, 2-,6- or 12-fold symmetry and square lattices having 0-, 2-, 4-or 8-fold symmetry can be analysed.

REGULAR directs the 'regular' MICRETE calculation. It alsocauses bucklings, in cases where only one type of fuel isconsidered, to be computed and optionally computes the levelcoefficient of reactivity.

INSUM generates an interpreted summary of MICRETE user inputand writes this summary to the output file (TAPE6).

RODMAP generates a rod map given the geometry and rodposition/type data.

5 - 2

CONTRL controls the MICRETE calculation iterative process.It interfaces directly with the subroutine MICRETE, whichperforms the actual calculations (Section 4).

MICRETE performs the MICRETE calculation according to theparameters passed to it by CONTRL. It sets up and solves thesystem of equations described in Section 4 of this report, andReference 2, page 4 and pages 19-20. (Central memoryrequirements are minimized by buffering problem coefficients onTAPE1, TAPE2, TAPE3, TAPE4, TAPE8 and TAPE9.)

COEFS uses rod and cell parameters to compute the MICRETEequation coefficients detailed in Reference 2, pages 19-20.

RAMP computes the reflector parameters F, I and J(Reference 2, pages 15-18 and pages 26-27).

RAMPP computes the reflector parameters F*, I* and J*(Reference 2, pages 15-18 and pages 26-27) associated with coreasymmetry.

MMPY performs the matrix manipulations needed to set up thevarious problem coefficient matrices. To minimize centralmemory requirements, coefficient data are buffered on thelogical files, TAPE1, TAPE4, TAPE7 and TAPE9.

MATRIX recovers MXY and MXW problem coefficient data writtento TAPE1 and TAPE8, and sets up the problem matrix MXX, bymultiplying MXY by W, subtracting MXW and dividing the result by10.

LINEQN optionally solves a system of linear equations usingGaussian elimination (IND=1), or computes the determinant of thecoefficient matrix (IND=2).

DETER causes the determinant of the coefficient matrix of asystem of homogeneous linear equations to be computed, given anestimate of a system eigenvalue.

OUTSOLU prints a summary of fluxes and related parametersassociated with the solution to the current MICRETE problem. Italso causes rod surface fluxes (SURF=1), or powers (PPOW=1) tobe computed.

SURFLUX computes the rod surface fluxes, given the rod axisfluxes.

POV>'ER computes rod powers, given the rod axis fluxes andpower factors.

BUCKLNG optionally computes Juf Jn+I0 and/or materialbucklings for lattices consisting of one type of fuel only.

5 - 3

BJNOT calculates the JQ Bessel function of argument X usingthe series:

- (X2/(22*l!2)) + (X4/(24*2!2)) - (X6/(26*3!2)

SUBSTIT directs the 'substitution' MICRETE calculation. Thiscalculation is a three step calculation. First, a referencelattice is modelled by adjusting the reference (type 1) rodresonance escape probability until the Jg-buckling matches themeasured buckling. Second, the substitution lattice ismodelled. Test fuel (type ITER) is substituted for referencefuel and the test fuel resonance escape probability is adjusteduntil criticality is achieved. Third, all reference fuel isreplaced with test fuel and the resulting assembly modelled byadjusting moderator height until criticality is achieved. Ifthis calculation fails, a large test lattice calculation isattempted. Upon successful completion of either the small orlarge core test calculation, JQ, JQ+IQ a n d material bucklingsare computed.

To further assist those who must maintain and/or extendMICRETE, a subprogram call map, a common block map and a symbolmap are reported in Appendix A. In addition, a Version 4.1program source listing is reported in Appendix B.

5.2 Memory Limitations

The use of fixed array dimensions limits the size andcomplexity of the lattice that can be modelled withoutrecompiling MICRETE. To simplify the task of changing MICRETEarray dimensions, all limiting dimensions have been specified interms of the constants NSEC, NTYP, NPTS and NBES (Symbol Map,Appendix A) that are defined in FORTRAN V PARAMETER statements(Program Listing, Appendix B).

5 - 4

Figure 5-1Program Hierarchical Diagram

o

A - 1

Appendix AProgram Maps

A - 2

To assist those who must maintain MICRETE Version 4.1, threeprogram maps are provided in this appendix. The first, the CALLMAP, illustrates the linkage among the various MICRETEsubprograms. The second, the COMMON BLOCK MAP, shows in whichroutines the various common blocks have been declared. Whilethe third, the SYMBOL MAP, lists all the symbols used inMICRETE, identifies where they are referenced and defines each.In addition, each symbol name is followed by a two charactertype designator. The first character indicates whether thesymbol represents a type Real, Integer, complex, Doubleprecision, jJoolean or Character variable. The second" indicateswhether the represented variable is a Scalar or an Array. Eachindicated reference is typed by three characters. An 'X' underDEFINED indicates that the symbol is defined in the referencedsubprogram. An 'X' under USED indicates that the symbol is usedin the referenced subprogram. Otherwise, the symbol isundefined and/or unused. The third character, the referencetype character, can have one of five possible values:

1 - (blank) indicates the symbol represents a localvariable

2 - 'C indicates the symbol represents a commonblock variable

3 - 'P' indicates the symbol represents a formalparameter

4 - 'D' indicates the symbol represents a dummyargument

5 - 'S' indicates the symbol represents a'stray' variable.

For complete definitions of local variable, common block, formalparameter, dummy argument and 'stray' variable, the reader isreferred to the CDC FORTRAN V Reference Manual.

A - 3

Table A-lSubprogram Call Map

W O pa OS H M

w D o: hj a

OOfrWO JQHf W«>JHZ BOS

XXX

X

S Ed XOS «C E Oi 0>

(J O H hoiS H O OJMEHMO C Z E- « J

X X X X X XXXX XXX

M zoi a s

O WO SH « ><OiOl XHKPIUtAUlM X X tvQ U H K H Z

X 5X X

iIlOOff iII O O OI Hi oon ii

I O O O HI »I O O H Rt H[ © O (N »I O O N II tlI Q O CN HI Mi o o o nI HI O O O H1 H| © O r-1 HI flI O O rH Hi nI o o r-t n1 O O f- «i nI 00(0 1i ni o o o NI N| O O . N |I Ni o o m ni ftI O O N I! Hi c o o nl O O l l

<COMHON BLOCK MAP>

IIIIIIIII

COMMONBLOCK

I SUBPROGRAMII M E Ü E I P G R I R C M C R R M M L D O S P B B SI A R S X K S E E N O O I O A A M A I E U U O U J UI I R E X B M O G S D N C E H H P T N T T B W C N BI N O R 2 E M U U M T R F P P Y R E E S F E K O SI R I S T L M I R E S P I Q R O L R L T TI S N S R A P L T X H L U H I

Y R • E 0 X G T

DATIHI TITLESI LATDATAI GEOPROPI ITCHTRLI HODPROPI REFPROPI RODCELLI KODPOSI FLXDATI OTHERSI BESSELI LEVCOEFI EIGENI COEPMATI REFL1I REFL2I HICCOEF

I NO. OF X100I COMMON X10I BLOCKS XI

-II XIIIIIIIIII •

IIIIIII

XX

XXXX

XX

X

X

XXXXXXXXXXX

X XX

XX

XX

X

XX

XXXXXXXXXXXXXXXX

X

X

XX

X

XX

XX

X

XX

XX

XXX

XX

X

X

XXXX

XXX

XXXXXXXX

XXX

XXXXX

XX X X

I O O O O O O O O Q O 0 0 O 0 O O O O O O O O O 0 0I 0 0 1 0 0 0 0 O 1 O 0 1 O O O 0 0 O 0 0 0 0 0 0 01 1 0 0 0 0 0 6 4 1 3 7 6 4 5 5 2 2 2 0 7 8 4 8 0 8

II

NO. OF iTIMES IREF D I

IIII1IIIIIIIIIIIIIIIIII

1

III

002002005014009008008008010014008002004002004003005005

OO

O H

crI-1 0)

oo >

to

<SYMEOL MAP>

I SYK20L1

REFERENCES

NAME

: I: I:T I:Y I:P I:E I: I: I

:E: ::F:U:T I

SUB- :I:S:Y I SUB-PROGRAM :N:E:P I PROGRAM

:E:D:E I:D: : I: : : I

D: : IE: : IP:U:T II:S:Y IN:E:P IE:D:E ID: : I: : I

SUB-PROGRAM

III1

: I: I

U:T IIIIII

S:YE:P

DEFINITION

IIIIIIIIIIII-IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

AII AI AAII AALIIIIIII AIII AilAJZALPHA

AARYABC

AHA1

ALPBADP

ALPHAF

ALPBAP

AlIISTRO

ASARGARR

I AlI BIII BII

: I:RS I; I:RS I:RS Ij I:RA Ii I:RA I1RS I: IsRS I

I:RA I: I:RS I:RS I:RS I: I: I:RS I: I: I:RS I: I: I:RS I: I.:RS I: I:RS I:RS I:RA I:RS I:RS I: I: I:RS I: I

I

COEFS

PSMÇOEFS

MICRBTESURFLUXCOEFSMICRBTE

EXX2

MICRETESURFLUXOUTSOLDBUCKLNGCONTRLSUBSTITRAMPRAMP

:X:X::X:X:

: : :C: : :C: :X:P:X:X:: : :: :X:P: : :: : :C: :X:C:X:X::X:X:: : :C: : :C: :X:C:X:X:

CONTRLSUBSTITRAMPRAMP

COEFS

MICRETERAMPPSMBUCXLNGBJNOTBUCKLNGCONTRLCOEPS

: :C: :C:X:C

:X:X:: : ::X:X:

ix.-x!:X:X:: :X:P:X:X::X:X:: : :C: .-X.-C: :X:P

COBFSPOWER

COEFSPOWERSURFLUX

MICRETEUSERINRAMPPRAMPP

MICRETEUSERINRAMPPRAMPP

RAMPP

USERINSUBSTITMICRETE

X: :C: :C

: :: :: :: :

X: :C:X:C

X:X:

! :CX:XiC:XiC

X:X:

:C:X:XiC:X:C

X:X:

IIIIIII OUTSOLUIIIIIII OUTSOLUIIIIIIIIIIIII

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I0(KU*A)MODIFIED BESSEL FUNCTION COMPUTATION SWITCH(1 - COMPUTE 10, 2 - COMPUTE II, 3 - COMPUTE K0OR 4 - COMPUTE Kl)I0(K*A)I0(KF*A)TEMPORARY VARIABLETEMPORARY VARIABLEFIRST BUCKLING POINT COORDINATE

SECOND BUCKLING POINT COORDINATE

THIRD BUCKLING POINT COORDINATE

FIRST BUCKLING POINT ORDIHATESECOND BUCKLING POINT ORDINATETHIRD BUCKLING POINT ORDINATEUSER INPUT DATA RECORD NUMBERTEMPORARY VARIABLETEMPORARY VARIABLETYPE NUMBER OF TYPE <ITER> ROD

POINTER TO TYPE <ITER> ROD DATA

IIIIIIIIIIII

-IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

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I SYMBOLIIIIIt NAMEIIII

II ITPNTIIII

REFERENCES

: I •: I:T 1:Y I SOB-tP I PROGRAM<E It II I

:D: : I:E: : I:FsU:T I!l:S:Y I

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SUB-PROGRAM

I : i

:F:U:T

:N:E:P I:E:D:E I:D: : I: : : I

DEFINITION

I VOLI II IRA

I 11KBI I1KBA

11MBI1RFBBIXRLCI1KDA

IIIII JIIII JI 3KtiI JAVPII JtI JJI JMAXIIIXI J lt KI *I KI KBMtti mntii wi »•**

i

t II It Itis :l IS I• RS IIRS IiRS tiRS:RStRSIRSI IS II . II I< I• RS ItRSIIRS II I(IS IlIS Iits tI Itt

INSUMBUCKLNGUSBRINLINIQHCOIFSCOBTScoirsCOIFS

i coirsI COIFSI COIFSUSIRINIHStMMATRIXBUCKINGRAMP

I KICRITBIKICRKI

I t iCI s tC|X:X:I :X:tX:XiiXtXtiXlXiiXtX:iXtXitXlX.tXtXtiXtX:

MICRETESUBSTIT

INSUIL1N1QNDSERIHSUBSTIT

I MIVXi ooTtonnI BDCKMIQ

l I S I UNION:I3 I HO*tRS I NXOUTBt I MCRLMG<KS I RM»»RS I MICMIII I MKH<n i Micxm< i«RS i constR8 I NICItRI<n i MICNRIt It I

iX:X:tXtXtP> >X:i s t> tXi< < ttXiXtiXtX:!X:XtCI sXtCi i :Ct : :C: t :C

< :Xt: :Xi:XiXt:XtX::XlX>cXtXiC: tXiCtXlXsC

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RAMPPRAMP

SURFLUX iXtXlPSH : :X:

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I RIGOLARILINEQNCOIFS

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IIII RANPPI COBFSI SOUFLOXI MNPII SURFLUXI COIFSI COIFSI 50RFL0XI

: IX::XsX:: : :<X:X:: tX:C: :X:C: :X:C: ! ::X:X:>X:Xi: :X:C: :X:C

5 5 !

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GEOHTRYMMpySUBSTIT

RAMPP

MICRETEROPHAPLINBQHPOKER

SURFLUX

RAMP

RANPP

: : : I: : :C I: :X:C I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : r I: : : I:X:X: I: :X: I

i : : I: : s I:X:X: I: : : I! : : I: : : I: : : I: : : I: :X:C I: : :C I: i :C I: : :C I: : : I: : : I: : ! I:X:X: I: : : Ij ; : I: :X:C I: : : I5 :XsC

SURFLUXRAMP s :XsC

USER INPUT DATA VOLUME NUMBERDO-LOOP CONTROL VARIABLEK*A*I0(K*A)K*B*I1(K*B)KBAR*A*I1(KBAR*A)KBAR*B*I1 (KBAR*B)KFBAR*B*I1(KFBAR*B)K*RLITC*I1(K*RLITC)KU*A*I1(KU*A)DO-LOOP INDEX VARIABLE AND/OR TEMPORARY VARIABLE

REFLECTOR COEFFICIENT J, REFERENCE 2, PAGE 26REFLECTOR MONOPOLE CALCULATION J, REFERENCE 2,PAGE 27REFLECTOR DIPOLE CALCULATION J*, REFERENCE 2,PAGE 27TEMPORARY VARIABLETEMPORARY VARIABLENUMBER OF DIFFERENT ROD TYPES DEFINED IN USER INPUT

DO-LOOP INDEX VARIABLECELL RECIPROCAL DIFFUSION LENGTH, CM**(-1)CELL RECIPROCAL DIFFUSION LENGTH, CM** (-1)

REFLECTOR COEFFICIENT K, REFERENCE 2, PAGE 26CELL EFFECTIVE RECIPROCAL DIFFUSION LENGTH, CM**(-1)

REFLECTOR EFFECTIVE RECIPROCAL DIFFUSION J-ENGTB,CM**(-1)CELL EFFECTIVE RECIPROCAL DIFFUSION AREA, CM**(-2)CELL RECIPROCAL SLOWING-DOWN LENGTH, CM** (-1)CELL EFFECTIVE RECIPROCAL SLOWING-DOWN LENGTH,CM** (-1)

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<SYMBOL MAP>

II SYMBOLII —-IIII NAMEIIII

II KFBARRII KFBARSQII KFRI KFSQI KINFI KINFIII KINFAI KKI KKI KKFI KKKI KNKAI KNKBAI KRI KSQI KOI KOIII KOAI KOSQI KlI KlKAI K1KBI K1KBAI K1KBBI K1KFBBI K1KLCII K1OI1I K10II KllII K2I

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:

:

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III

IIIIIIII

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

SOB-PROGRAM

HICRETE

COEFS

MICRETECOEFSCOEFSUSERINHICRETEBOCKLNGCOEPSLINEQNGEOMTRYGEOMTRYGEOMTRYCOEFSCOEFSMICRETECOEFSCOEFSDSERINHICRETEBOCKLNGCOEFSCOEFSCOEFSCOEFSCOEFSCCEFSCOEPSCOEFSHICRETESORFLOXCOEFSMICRETESDRFLOXMICRETESORFLOXMICRETE

:D: : I:E: : I:F:O:T I:I:S:Y I:N:E:P I:E:D:E I:D: : I: : : I

: : : 3:X:X:C I: : : I:X:X: 1: : : J:X:X: ]:X:X: I:X:X: ]:X:X:C ]: :X:C ]: :X:C ]: :X:P ]:X:X: ]: :X:C ]: :X:C J:X:X: ]:X:X::X:X: ::X:X::X:X::X:X::X:X:C: :X:C: :X:C: :X:P:X:X::X:X::X:X::X:X::X:X::X:X::X:X:: :X:C: :X;-C:X:X:: :X:C: :X:C: :X:C: :X:C: :X:C: : :

REFERENCES

SOB-PROGRAM

RAMP

SORFLOX

SORFLOX

INSUMSORFLOXSOBSTIT

HICRETE[ HICRETEBUCKLNG

; SORFLDX

; INSOHC SORFLOXI SOBSTITIIIIII SORFLDXI SORFLOXI SORFLOXI COEFSI POWERII COEFSI POWERI COEFSI POWERI COEFSI

:D: ::E: !:F:O:T: I:S:Y:N:E:P:E:D:E:D: :: : :

: : :: :X:C: : ::X:X:r : :: : ::X:X:: : :: :X:C: :X:C:X:X:C; • ;: : ::X:X:C:X:X:C:X:X:s : ::X:X:: : *:: : :: : :: IXIC: :X:C: :X:C; . ;: : :: : !: : :: : ::X:X::X:X::X:X::X:X:C: :X:C: : ::X:X:C: :X:C:X:X:C: :X:C:X:X:C: : :

IIIIIIII


:•D: :B: ::P:OsT

SOB- :PROGRAM :

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RAMPP :

CONTRL !POWER

CONTRLPOWER

OOTSOLO

OOTSOLO

OOTSOLO

OOTSOLO

I:S:YN:E:PE:D:ED: :

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IIIT

IIIIIIII


DEFINITION

REFLECTOR EFFECTIVE RECIPROCAL SLOWING-DOWNLENGTH, CM**(-1)CELL EFFECTIVE RECIPROCAL SLOWING-DOWN AREA,CM**(-2)REFLECTOR RECIPROCAL SLOWING-DOWN LENGTH, CM** (-1)CELL RECIPROCAL SLOWING-DOWN AREA, CM**(-2)CELL K-INFINITYCELL K-INFINITY

CELL K-INFINITYINDEX VARIABLEKO(KBAR*LITT)KO(KBAR*LITT)INDEX VARIABLEK0(K*A)KO (KBAR*A)REFLECTOR RECIPROCAL DIFFOSION LENGTH, CM** (-1)CELL RECIPROCAL DIFFOSION AREA, CM** (-2)KU, REFERENCE 2, PAGE 23KO, REFERENCE 2, PAGE 23

KD, REFERENCE 2, PAGE 23KO**2DPOD*GAM* (1-K1KFBB) + DFOD* (GAM+PSI) * (1-K1KBB)K*A*K1(K*A)K*B*K1(K*B)KBAR*A*K1(KBAR*A)KBAR*B*K1(KBAR*B)KPBAR*B*K1(KFBAR*B)K*RLITC*K1 (K*RLITC)

K1(K*B)/I1(K*B)-P2*K5

P2*K6 + K8

(EOA*A)/(D*(KOSQ-KBARSQ))

IIIIIIIIIIII

IIIIIIIIIIII

' IIIIIIIIIIIIIIIIIIIIIIIIIIIII

O"en n>

3 >O u>

3 OO) O

«SYMBOL MAP>

SYMBOL REFERENCES

I1 NAMEII

:T

:P:E

K2K3K3M

K5

• :E: :

SUB- :I:S:YPROGRAM :N:E:P

:E:D:E:D: :.: : :

:O: : I:E: : I:F:O:T I

SOB- :I:S:Y IPROGRAM :N:B:P I

:E:D:E I:D: : I: : : I

:PSUB-PROGRAM

:E

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KSK9

I K6I K7IIIII LI LI LI LAMIII •

II LASTI LATAKNGIII1IIIIIIIIIIIIrii

LCHRCNTLCRIND

LFCASQLFCASQ

LFCASQALFCRSQLFCRSQ

LFCRSP".

:IS I:RS I:RA I: I:RS I:RS I:RA::RS:RA

:RS I: I: I: I: IiIS I:1S I: I: I: I: I:IS I:IS I: I: I:RS I:RA I: 1: I:SA I:RS:RA I

I: I: i

:RA I: I

SORFLDXBOCKLHGCOEFSMICRETESDRFLDXCOEFSCOEFSMICRETESURFLOXCOEFSMICRETESDRFLDXUSERINGEOHTRYRAMPOSERININSUMMICRETERAMPPBOCKLNGBOCKLNGGEOMTRYCONTRLRAMPSURFLUXDSERININSUMGBOMTRÏBOCKLHGREGULARCOEFSDSERINMICRETEBDCKLNGCOEFSCOEFSUSERINMICRETEBDCKLNGCOEFS

: :X:C:X:X::X:X:: :X:C: :X:C:X:X::X:X:s :X:Cs :X:C:X:X:! :X:C: :X:C

IIIII COEFSI POWERIIIIII COEFSI POWER

POWER

COEFSPOWER

:X:X::X:X:C: :X:C: :X:C: :X:C: :X:C:X:X:: : :C: : :Cî : :C: : :C:X:X:C: :X:P: : :C: : :C:X:X:C:X:X::X:X:C: :X:C: :X:C: :X:P:X:X::X:X:C: :X:C: :X:C: :X:P

I MICRETEI RAMPPGEOMTRYRODMAPCOEFSODTSOLUSOBSTIT

: : ! I: iX:C I: : s I: : : I:X:X:C I: :X:C 1: : s I: : s I:X:X:C I: :X:C I: : : I:X:X:C I: tXsC I

IIII

REGULARMICRETERAMPPBOCKLNGINSUM

MICRETESUBSTITINSUM

INSUMSURFLUXSUBSTIT

INSUMSURFLUXSUBSTTT

:X:X::X:X:: :X:C: :X:C I: :XsC I: :X:C It :X:C I: : s I: : :C I: : :C Is : sC I: : :C I: :X:C I: : : I: :C I: :C I:X:C I: : I

II: :XiC

: :X:C:X:X:C I: : s I: : : I: :XsC I: :X:C:X:XsC I: : î I: ! i I

CONTRLPOWER

DEFINITION

OUTSOLD

OUTSOLU :X:C: :

REGULARCONTRLRAMPSURFLUX

RODMAPCOEFSOUTSOLDSOBSTIT

OOTSOLOUS2RINCONTRL

CONTRLPOWER

:X:C I: : I: : I: : I:X:C I: : I

III

: : : I: : : I: : s I: :X:C I: :X:C I: :X:C I: :X:C I: : : I: : : I: : :C I: : :C I: : :C I: : :C I: : : I: : : I: : :C I:X:X:C I: :X:C I: : : I:X:X:C I: :X:C I: : : I: : : I: : : I: :X:C I: :X:C I: : : I: : : I: : : I

1-(INKOA*K1KBA + I1KOA*KNKA)1-(INKOA*K1KBA + I1KOA*KNKA)K1*P2 + BOA*P2*P5*DFOD*KFBARSQ/KBARSQ

DFOD*GAM*I1KFBBDPOD*{GAM+PSI)•I1KBBK2*(I1KOA*INKA - INKUA*I1KA)

BOA*P2*I1KBB*DFOD*KFBARSQ/KBARSQ-DFOD*PSI*KBAR*RLITC*I 1 (KBAR*RLITC)

DO-LOOP INDEX VARIABLEDISTANCE FROM ROD-I TO ROD-J IN LATTICE SPACESREFLECTOR COEFFICIENT L, REFERENCE 2, PAGE 26LATTICE SPACING, CM

INDEX VARIABLELATTICE ARRANGEMENT, DEGREES (60-HEXAGONAL, AND90-SCTJAHE)

NUMBER OF CHARACTERS IN OUTPUT BUFFER LINOUTLEVEL COEFFICIENT OF REACTIVITY CALCULATION SWITCH<1«ON, 0»OFP)

CELL AXIAL SLOWING DOWN AREA, CM**2CELL AXIAL SLOWING DOWN AREA, CM**2

CELL AXIAL SLOWING DOWN AREA, CM**2CELL RADIAL SLOWING DOWN AREA, CM**2CELL RADIAL SLOWING DOWN AREA, CM**2

CELL RADIAL SLOWING DOWN AREA, CM**2

IIIIIIIIIIII-IIIIIIIIIIIIIIIIItItIIIIIIIIIIIIIIIIIIIIIII

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2 OCJ O

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<SYMBOL MAP>

NAME

I SYMBOLIIIIIIIIIIIIIIIIII

rI LLII LHAXIII LSQIII LSQMIII LSQRIIIIIIIIIIIIIIIIIIIII

REFERENCES

'. I: I:T I:Y I

IIII

sPsG:s

SUB-PROGRAM

:D: : I:E: : I:FiU:T I:I:S:Y I:N:E:P I:E:.T:E I:D: i I: : : I

SUB-PROGRAM

:D: ::E: ::F:U:T

iN:EiP:E:D:E

:F:U:TSUB-PROGRAM :N:E:P

:E:D:E

DEFINITION

IIIIIIIIIIII

-IIIIIIIIIIIIIIIII1IIIIIIIIIIII

LPSQ

LINCNTLINOOTLITT

LSSQC

LSSQM

LSSQR

LI

HMAXMXU

MXW

: I:RS I: Is I:IS I:CS I:RA I: I:IS I: I:IS I: I: I:RA I• I

: I:RS I: I: I:RS I: I

II

s I: I:RS I: I: I:RS I: I: I:RA Is I:IS I: I:RS I:RS I•.RA I

I:RA I

USERINCOEFSSURFLUXRODKAPRODMAPGEOMTRY

: : : I: :X:C I: :X:C I: :X:C I:X:X::X:X::X:X:C

::RS

CONTRL :X:X:

MICRETESURFLUXGEOMTRYUSERINMICRETEBUCKLNGUSERINCOEFSSURFLUXUSERINMICRETEBUCKLNGUSERINCOEFSSURFLUXUSERINCOEFSSURFLUXUSERINMICRETEBUCKLNGMICRETESURFLUXRODMAPSURFLUXRAMPLINEQNMICRETELINEQNMICRETE

IIIIII

: :X:C I: : :C I:X:X:C I.-X.-X.-C I: :X:C I: :X:C I:X:X:C I: :X:C I: :X:C I:X:X:C I: :X:C I: 1X1C I:X:X:C I: 1X1C I: :X:C I:X:X:C I: :X:C I: :X:C I:X:X:C I: :X:C I: :X:C I: :X:C I: :X:C I: :X: IX:X: I:X:X: I:X:X: I:X:X:C I: !X:C I:X:X:C I: : : I

INSUMRAMPBUCKLNG

INSUMMICRETE

USERINBUCKLNGINSUMINSUMSURFLUXSUBSTITINSUMRAMPBUCKLNGINSUMRAMPSUBSTITINSUMRAMPBUCKLNGINSUMRAMPBUCKLNGINSUMRAMPSUBSTITCOEFSPOWERMICRETE

RAMPP

MMPY

MMPY

:X:C:X:C:X:C

:X:P:X:C

: :C: .:C:X:C:X:C:X:C:X:C:X:C:X:C:X:C:X:CI X I C

:X:C: :X:C: :X:C: :X:C: :X:C: :XsC: :X:C: :X:C: :X:C: :X:C:X:X:C: :X:C:X:X:

MICRETEII1IIIIIIIIIIIIIIIIIIII MICE2TE

CONTRLSUBSTIT

CONTRLPOWERCOEFSMICRETERAMPP

CONTRLRAMPP

:X:X:C I: :X:C I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : :C I

: :C I: : I:X:C I:X:C I:X:P I:X.-C I:X:C I: : I:X:C I:X:CI: : I:XsC I:XsC I

I RAMPPI : : !I MICRETE : :X:CI RAMPP : :X:CI : : :I CONTRL : :XsCI RAMPP : :X:CI : : :I OUTSOLU : :X;CI : : :I OUTSOLU :X:X:

: : : I : : ::X:X: I : : :: : : I : : ::X:X:C I MATRIX : :X:C: : : I : : :: :X:C I MATRIX :X:X:C: : : I : : :

CELL SLOWING-DOWN AREA, CM**2

TEMPORARY VARIABLEOUTPUT BUFFERDISTANCE FOR WHICH KO BESSEL FUNCTION MUSTBE CALCULATED, CMITERATION LOOP COUNT. IF LL IS GREATER THAN 20,THE MICRETE IS CONSIDERED TO HAVE FAILED.NUMBER OF DISTANCES FOR WHICH KO BESSEL FUNCTIONEVALUATION IS NECESSARY

CELL DIFFUSION AREA, CM**2

MODERATOR DIFFUSION AREA, CM**2

REFLECTOR DIFFUSION AREA, CM**2

TYPICAL CELL SLOWING DOWN AREA, CM**2

MODERATOR SLOWING DOWN AREA, CM**2

REFLECTOR SLOWING DOWN AREA, CM**2

K2*K3

TEMPORARY VARIABLE

REFLECTOR COEFFICIENT M, REFERENCE 2, PAGE 26TEMPORARY VARIABLEPROBLEM COEFFICIENT MATRIX COLUMN/ROW

PROBLEM COEFFICIENT MATRIX COLUMN/ROW

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(SYMBOL MAP>

SYMBOL REFERENCES

NAME

IIII

MXWMXX

HXY

NN

I NI NI NI NBESIIIII1 NCRDII NEWZI SII NMAXIIIII1IIIII

NN1

NPTL

IIII NPTSIIII

:T:Y:P:E

:E: ::F:U:T

I SUB- :I:S:YI PROGRAM :N:E:PI :E:D:EI :D: :I : : :

IIII SUB-I PROGRAMIII

:F:U:T:I:S:Y:N:B:P:E:D:EsD: :

IIII SUB-I PROGRAMIII

:D: : I:E: : I:F:U;T I:I:S:Y I:N.-E:P I:E:D:E I:D: : I

DEFINITION

:

:RA::RA

:RS

LINEQNMICRETELINEQNHICRETELINEQNRODMAPPSHMAINRAMPGEOHTRYUSBRINCOHTRLMATRIXSURFLUXSUBSTIT

I MICRETEI MAINI REGULARI CONTRLI GEOHTRYRODMAP

I GEOMTRYMATRIXSURFLUXSUBSTITSUBSTITREGULARMICRETELINEQNPOWERREGULARMMPYUSERINRODMAPSURFLUXSUBSTITREGULARMMPYUSERINRODMAP

: :X:C:XtX:C:XiX:C:X:X:C: :X:C: :X:: :X:P: :X:S:X:X::X: :S

:X:X:X:X:: :X:P:X:X::X:X::X:C

X: :C: :C: :C-. iC:X:C: :C: :C: :C: :C

MMPY

POWER

:X:X:C: : ::X:X:C

:X:X::X:X:

:X:X:

:X:X::X:X:

RAMPP :X:X:

REGULV. :X: :COEFS :X: :LINEQN :X: :POWER :X: :GEOMTRY :X:X:

ERRORSSUBSTIT

MICRETEREGULARLINEQN

I POWERINSUMUSERININSUM

I MMPYOUTSOLUBUCKLNGCONTRL

I MATRIXGEOMTRYMICRETEPOWER

CONTRLMATRIXGEOMTRYMICRETE

:X:P:X:P

:X:C: :C: :C: :C:X:C

X: :C: !C: :C: :C: :C

:X:X::X:X::X:X:

:X:X::X:X:

MATRIX

MATRIX

RODMAPMMPYOUTSOLUBUCKLNGINSUM

USERIN

: : : I: : : I:X:X:C I: : : I:X:X:C I: : : I: : : I: : : I: : : I: : : I: : : I:X: : I:X: : I

: I: I

USERINMMPYOUTSOLUBUCKLNG

GEOMTRYRODMAPMATRIXSURFLUX

COEFSLINEQNINSUMOUTSOLUBUCKLNG

COEFSLINEQNINSUMOUTSOLU

:X:X: I: i : x:X:X:P I: : : I: : : 1: I : 1: : :C I: ! :C I: : :C I: : :C I: : : I: : :C I: : :C I: : :C: : iC

:X:X::X:X::X:X:

:X:X::X:X:

PROBLEM COEFFICIENT MATRIX

PROBLEM COEFFICIENT MATRIX COLUMN/ROW

TEMPORARY VARIABLEORDER-1 OF POLYNOMIAL BEING EVALUATEDTEMPORARY VARIABLEREFLECTOR COEFFICIENT N, REFERENCE 2, PAGE 26TEMPORARY VARIABLEMAXIMUM NljrtBER OF BESSEL FUNCTION EVALUATIONS

USER INPUT CARD NUMBER

PROBLEM DETERMINANT CURRENT ITERATIONTEMPORARY VARIABLENUMBER OF RODS IN PROBLEM LATTICE

NUMBER OF RODS IN LARGE TEST LATTICE SECTOROF SYMMETRY, SUBSTITUTION CALCULATION ONLY

MAXIMUM NUMBER OF ADDITIONAL CELLS IN "LARGE" CORECALCULATION - SUBSTITUTION MODE>

MAXIMUM NUMBER OP RODS IN REACTOR LATTICE

IIIIIIIIIIII

-IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

3cu

crt-1

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«.SYMBOL MAP>

II SYMBOLI

IIIIIIII

REFERENCES

NAME

NPTS

HSEC

NT

IIIIIIIIIIIIIIII NTYPIIIIII NlIriiiiiiI OTTOII PI PI PIIII PAI PARAMII

I: I:T I:Y I SÜB-:P I PROGRAM

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SOB-PROGRAM

:P:O:T:I:S:Y:N:E:P:E:D:E

IIII SÜB-I PROGRAMIII

III1

:D: : I:E: : I:F:O:T I:I:S:ï I:N:E:P I:E:D:E I:D: : I: : : I

DEFINITION

: I: I:IS I: I: I: I: J: I:IS I: I: I

N2OLDZOPTION

:RS:CS

:RS::RS:RS:RA I: 1: I: I:RA I:IS I: I: I

SURFLUXSOBSTITOSERININSUMMICRETEMATRIXSURFLUXSUBSTITREGULARHHPYOUTSOLUGEOMTRYMICRETESUBSTITGEOMTRYMMPYOSERINMICRETESURFLUXSUBSTITUSERINMICRETELINEQNPOWERRODMAPGEOMTRYCONTRLMAININSUMMICRETEOUTSOLUCOEFSRAMPPOWERGEOMTRYMICRETEBUCKLNGCOEFSUSERININSUK

:X:X::X:X::X:X::X:X::X:X::X:X::X:X::X:X:

:X:X::X:X::X:X:

:X:X::X:X::X:X::X:X::X:X:C I:X:XiC I: :X:C I: :X:C I: : iC I:X:X: I:X:X: I:X:X: I: :X:P I: : :C I:X:X:C I:X:X::X:X:: : :C:X:X:C: .-X.-C: :X:C: :X:P I:X:X:C I: :X:C I: : : I

POWER

GEOtaTRYRODMAPCOEFSLINEQNPOWER

RODMAPMATRIXPOWERINSUMSURFLUX

REGULARMATRIXINSUMCOEFSPOWER

GEOMTRYMMPYOUTSOLOBUCKLNGINSUM

USERINCONTRLREGULAR

:X:X:: : ::X:X::X:X::X:X::X:X::X:X:

BUCKLNG :X:X:

REGULARCONTRL

I MMPY

RAMFPSUBSTITINSUMOUTSOLO

GEOMTRYCONTRL

:X:X::X:X:

:X:X::X:X::X:Xi

i ixlc: :X:C: :X:C

:X:C:X:C

:X:X:P: :X:P: :X:C

:X:X::X: :C: :X:C: :X:C

: :X:C:X:X:C

OUTSOLUBUCKLNG

COEFSLINEQNUSERINCONTRLBUCKLNG

RODMAPLINEQNCONTRLOUTSOLUBUCKLNG

REGULARMATRIXSURFLUXSUBSTIT

:X:X::X:X::X:X::X:X::X:X:

REGULARSUBSTITCONTRL

USERINRODMAPSURFLUX

REGULARMICRETE

IIIIIIIIIIIIIIIIIIIIIIIII

: : : I: : : I: s : I: :X:P I:X:X:P I:X:X:C I: ! : I: : : I: ! : I:X:X:C I: :X:C I: :X:C I: : : I: : : I:X:X:C I: :X:C I: : : I

:X:X::X:X::X:X:

:X:X::X:X::X:X:• : •

: :X:C: :X:C: :X:C:X:X:C

MAXIMUM NUMBER OF RODS IN A SECTOR OF SYMMETRY

MAXIMUM ALLOWED NUMBER OF LATTICE PITCHES BETWEENROD SITES

MAXIMUM NUMBER OF UNIQUE ROD/CELL TYPES

NUMBER OF RODS IN SECTOR OF SYMMETRY

TEMPORARY VARIABLEPROBLEM DETERMINANT PREVIOUS ITERATIONCURRENT MICRETE CALCULATION MODE, EITHER REGULAROR SUBSTITUTECURRENT VALUE OF ITERATION PARAMETER

ROD COORDINATE POSITIONREFLECTOR COEFFICIENT P, REFERENCE 2, PAGE 26ROD COORDINATE POSITION

CELL RESONANCE ESCAPE PROBABILITYITERATION PARAMETER SELECT SWITCH

IIIIIIIIIIII

-IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

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3 >cr Io u>

3 nD) O

<SYMBOL MAP>

SYMBdL

NAME

II PARAMI PAXISI PEI PHIIIIII PIII PIHI PLIIIIIIIII

REFERENCES

PLACE

PMAXPOWPOWW

I PPIIIIII PSIPSHPiP10

PPHIPPOW

IIII1 P2II P3II P4II P5I QI

:;:T:Y:P:E;••

.

•

:CS:RS:RA::;

• ;

:RS

:RS:RA;;

• IA:::RS:RA:RA:RA;J

:RA:RS;:RS:RS:RS:RAs:RA::R&;:RA::RS:RS

IIIIIIII

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

SUB-PROGRAM

ODTSOLURODMAPGEOMTRYUSERINRODMAPMATRIXBUCKLNGOUTSOLUREGULARBDCKLNGMICRETEGEOMTRYHI CRETEPOWERSUBSTITUSERINHICRETEBDCKLNGRODMAPOUTSOLUPOWERSURFLUXUSERINHICRETEOUTSOLUMICRETEINSUMCOEFSPSHCOEFSCOEFSPOWERODTSOLUCOEFSCOEFSPOWERCOEFSPOWERCOEFSRAMP

:D: ::E: ::F:D:T.•I.-SsY:N:E:P:E:D:E• Ds :: : :

: : :: zX:C:X:X::X:X:: : :C: : sC! : :C: : :C: :X:C:X:X::X:X::XtX:: : :C: : :C: : :C: :X:C:X:X:C: :X:C: :X:C:X:X:: sX::X:X:: t :C:X:X:C: :X:C: :X:: : :C: :X:C:X:X:;XS ;:X:X::X: :Cr : :C: : :C:X:X:C:X: :C: : :C:X: :C: : :C:X:X::X:X:

IIIIIIIM

1

IIIIIIIIIIIIIIIIIIIIIIIIIIIIII11IIIIIIIIII

SUB-PROGRAM

BDCKLNG

BUCKLNGGEOMTRYMICRETELINEQNSUBSTIT-SURFLtJXMICRETE

BUCKLNGINSUMOUTSOLUBUCKLNG

INSUMSURFLUXSUBSTIT

POWER

POWERINSUMSUBSTITSURFLUXSUBSTITOUTSOLDSURFLUX

OUTSOLUMICRETEPOWERSURFLUXOUTSOLDMICRETEOUTSOLDMICRETE

RAMPP

:D: ::E: ::F:U:T:I:S:Y:N:IJ.P:E:D:EsD: :: : i

. . .

: :x!c: : ::X:X:: : iC:X: :C: : :C: : :C: :X:C:X:X:: : ::X:X:: : *:C: : :C: s :C: : :: :X:C: :X:C: :X:C

: x ::X:X:P: : :: : :C: :X:C:X:X:C:X:X:P: : :C: :X:C:X:X:• • :: : :: : :C: :X:C: : :C: :X:C: : :C: :X:C: : :C: :X:C: r ::X:X:

IIIIIIII

IIIIIIIIIIIIIIIIIIIIIIIIIIII]1]]]]]]

:

SUB-PROGRAM :

:

SUBSTIT :

INSUM iMMPY :POWER :REGULAR :

COEFS :

RODMAP :SURFLUX :USERIN :

CONTRL :POWER

BUCKLNGCONTRL

DSERIN

SURFLUX

MICRETE[SDRFLUX

SDRFLUX

E: :F:U:TIJS.-YN:E:PE:D:ED: :

• ••

. .

XiX:C

; •: :C: iC: :C:X:C• ;

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IIIIIIII

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

DEFINITION

COORDINATEROD COORDINATE POSITIONRELATIVE FAST FLUX, UNITLESS

3.1415926535898

PI*HROD COORDINATE POSITION IN LARGE TEST LATTICE,SUBSTITUTION CALCULATION ONLY

ROD TYPE INDEX

MAXIMUM ROD COODINATE POSITION, LATTICE PITCHESROD POWERREFERENCE ROD POWERCELL RESONANCE ESCAPE PROBABILITY

RELATIVE FAST FLUX ON ROD SURFACEROD POWER CALCULATION SWITCH (1-ON, 0=OFF)

KFSQ/KBARSQRESULT OF POLYNOMIAL EVALUATIONKINF*AAL/ (PI*BSQ*ANISTRO)1 - KBAR*RLITC*K1(KBAR*RLITC)

P1/(DF*KFBARSQ)

P2/(1-K1KFBB)

I1KFBB

1 - K1KBBREFLECTOR COEFFICIENT Q, REFERENCE 2, PAGE 26

cn n>

cro

3B)tf

1CO

(?O3

>

I

<SYMBOL MAP>

SYMBOL

NAME

IIII-IIIIIIII

iI QIIII QAXIS

REFERENCES

QL

QMAX

onI RIIIIIIIIIIIIItIII

RAO

RADIUSRCOR

:T:Y:P:E

SUB-PROGRAM

:D: : I:E: : I:F:U:T I:I:S:Y I:N:B:P I:E:D:E I:D: : I

S!IB-

:D: : I:E: : I:F:H:T I:I:S:Y I

PROGRAM :N:E:P I:E:D:E I:D: : I

SUB-PROGRAM

III1

:D: : I:E: : I:F:U:T I:I:SsY I:N:E:P I:E:D:E I:D: : I: : : I

DEFINITION

REFAMP1REFAMP3

I REFAMP4I REFAMP5I RBOIIIII RINBR1I RINBR2I

: I:RA I: I: I: I:CS I:RA I: I: I: I:RS I:RS I:RS I:RS I:RA I: I: I: I:RS I: I: I: I: I:RS I:RS I: I: I: I: I:RS I:RS I:RS I:RS I:RA I: I: I: I: IiRS I:RS I

POWERGEOMTRYMICRBTEBUCKLNGRODMAPGEOMTRYMICRETEPOWERSUBSTITRODMAPGEOMTRVMICRETERAMPDSBRINOOTSOLUBUCKLNGMICRBTEUSERINRODMAPCOEFSOUTSOLUSUBSTITOUTSOIUREGULARCOEFSBUCKLNGGEOMTRYRAMPMICRETEMICRETEMICRETEMICRETEUSERINRODMAPREGULARLINEQNPOWERBUCKLNGBUCKLNG

: : :C:X:X:C: :X:C: :X:C:X:X:: : iC: : :C: : :C: :X:C:X:X::X:X::X:X::X:X:: : :C: : :C: : :C: :X:C

: ': :C: : :C: : :C.- : :C:X:X:: : :C: : :C: : :C:X:X:C: :X:C:X:X::X:X::X:X::X:X:: : :C: : :C: :X:C:X:X:C: :X:C:X:X::X:X:

SUBSTITINSUMOOTSOLU

INSUMOUTSOLUBUCKLNG

RAMPPINSUMSURFLUXSUBSTIT

REGULARCONTRLRAMP "SURFLUXGEOMTRYSURFLUXRODMAPOUTSOLUSUBSTITINSUMRAMPP

GEOMTRYMATRIXMICRETEOUTSOLUBUCKLNG

I : I: :C I USERIN:X:C I RODMAP.-X.-C I SURFLUX: : I: : I: :C I RODMAP: :C I SURFLUX: :C I USERIN: ! I

:X:X:: : :C: : :C: : :C

RODMAPPOWERGEOMTRY

: sC I INSUM:C I MICRETE:C I

IRAMPPBUCKLNGsC

: :X:C I:X: :S I: : sC I MICRETE: : :C I SURFLUX: : :C I USERIN: :XiC I CONTRL: :X:C I: : : I: : : I: : s I: : : I: : sC I: : iC I:X:X:C I: :XiC I: :X:C

INSUMSUBSTITHMPYSURFLUX

! : : I!X:X:C I

:X:C I:X:C I: : I: : I: :C I: :C I

X1X1C I: : I: : I: : I: : I: : I: :C I: :C I

X:X:C I: : 1: :C I: :C I: :C I: :C I-• : I: : I: :C I: :C I

X:X:C IX:X:C I: : I: : I: : I: : I: : I: :C I: :C I

X:X:C I:X:C I: : I: : I: : I: : I

ROD ORD:;NATE POSITION

ORDINATEROD ORDINATE POSITION IN LARGE TEST LATTICE,SUBSTITUTION CALCULATION ONLY

MAXIMUM ROD ORDINATE POSITION, LATTICE PITCHESTEMPORARY VARIABLEDFOD*(KF/KBAR)* * 2REFLECTOR COEFFICIENT R, REFERENCE 2, PAGE 26DISTANCE FROM CENTRE OF LATTICE TO ROD, CM

EQUIVALENT RADIUS FACTOR (0.5250376 FOR HEXAGONALGEOMETRY AND 0.5641896 FOR SQUARE GEOMETRY)

DISTANCE FROM CENTRE OF LATTICE TO ROD, CMREACTOR CORE RADIUS, CM

KllK7-K9RELATIVE THERMAL FLUX, UNITLESS

TEMPORARY VARIABLETEMPORARY VARIABLE

IIIIIIIIIIII-IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

crCO fl>><3 >cr i

2 OQJ O•X3 3

<SYMBOL MAP>

I SYMBOLI

REFERENCES

- I - . -III

NAME:T:Y I:P I:E I: I: I

:F:D:TSUB- :I:S:YPROGRAM :N:E:P

:E:D:E

: : :

: D : : I: E : : IrF:O:T I: I : S : Y I

D:

SUB- :I:S:Y I SUB-I PROGRAM :N:E:P I PROGRAMI :E:D:E II :D: : II : : : I

IIIII

E: : IF:U:T II:S:Y IN:E;p IE:D:E ID: .• I: : I

DEFINITION

IIIIIIIIIIII

-IIIIIIIIIIIIIIIIIIIIIIIIIIIII

RINBR3I RJM.R1I EJNLR2I RJNI<R3I RKINFI

RLAMIP1RLAMIP2RLAHIP3RLCRRLITB

IIIIIII RLITCI

RMINRtiUMRODID

! I:RS I:RS X:RS I:RS I:RS I: I:RS I

BUCKLNG :X:X:BUCKLNG :X:X:BUCKLNG :X:X:BUCKLNG :X:X:BDCKLNG :X:X:

BUCKLNG :X:X::RS I BUCKLNG :X:X:

BUCKLNG :X:X:REGULAR :X:X:COEFS :X:X:

RODRAD

ROOT1 :RS

ROUTINERP

RRHORlR2

I SI SIIII SIG1I SIG2I SINNI

:RS I:RS I:RS I: I":RA I: I:RS I:RS I:RA I: I: I:RA I: I: I

I

: I:CS I:RS I: I! I:RA I:RS I:RS I:RS

MICRBTE : : :CSURFLUX : : :CGEOMTRY :X:X:BUCKLNG :X:X:CONTRL : : :CPOWER : : :CUSERIN :X:X:CPOWER : : :CUSERIN :X:X:CMICRBTE : :X:CBUCKLNG :X:X:

:RS:RS I:RA I: I

ERRORSMICRBTEINSUMRAMPPOUTSOLUBUCKLNGBUCKLNGRAMPUSERINRODMAPSURFLUXSUBSTITREGULARREGULARMICRBTE

: :X:P: : iC: :X:C: :X:C: :X::X:X::X:X:.-X.-X::X:X:C: :X:C: :X:C:X:X:C:X:X::X:X::X:X:

COEFSPOWER

MICRETEBUCKLNGINSUMBUCKLNGINSOMSURFLUX

BUCKLNGCONTRLSUBSTITSURFLUX

RAMPPGEOMTRYMICRETEPOWER

; i : I

: : : I: : : I: : : I: : : Ir : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I:X: iC I OUTSOLU: : :C I: : : 1: : : I: : :C I: : :C I.- :X:C I: : :C I: :X:C I: :X:C I: : : I: : : I: : : Is : :C 1:X:X:C I:X:X:C I:X:X:P I! : : I

SURFLUXSUBSTIT

SUBSTITCONTRL

USERINRAMP

:X.X::X:X:C: :X:C: :X:C

INSUMOUTSOLUBUCKLNG

: s I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: :C I: : I: : I: : I: :C I: :C I: : I: :C I:X:C I: : I: : I: : I: : I

X:X:C I:X:C I: : I: : I: : I: : I: : I:X:C I:X:C I:X:C I: : I: : I: : I

: : : I: : : I

TEMPORARY VARIABLETEMPORARY VARIABLETEMPORARY VARIABLETEMPORARY VARIABLEK-INFINITY COMPUTED FROM JO-BUCKLING AND TWO-GROUPCELL PARAMETERSFIRST BUCKLING POINT COORDINATE, CMSECOND BUCKLING POINT COORDINATE, CMTHIRD BUCKLING POINT COORDINATE, CMCOMPUTED LEVEL COEFFICIENT OF REACTIVITYROD EQUIVALENT RADIUS, CM, ASSOCIATED WITH RESONANCEABSORPTIONS, REFERENCE 2, PAGE 13ROD EQUIVALENT RADIUS, CM, ASSOCIATED WITH RESONANCEABSORPTIONS, REFERENCE 2, PAGE 13TEMPORARY VARIABLETEMPORARY VARIABLEROD IDENTIFIER (MAXIMUM 10 CHARACTERS) •

ROD RADIUS, CM

MATERIAL BUCKLING AS COMPUTED FROM 2-GROUP CELLPARAMETERS, M**(-2)NAME OF ROUTINE IN WHICH ERROR OCCURREDREFLECTOR OUTER RADIUS, CM

RELATIVE THERMAL FLUX ON ROD SURFACETEMPORARY VARIABLETEMPORARY VARIABLEREFLECTOR COEFFICIENT S, REFERENCE 2, PAGE 26ROD TYPE INDEX

SUM OF SQUARES OF RELATIVE THERMAL FLUXESSUM OF PRODUCT OF RELATIVE FAST AND THERMAL FLUXESROD POSITION DIRECTION SINE

v

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o to

3 O01 O"O 3

<S MBOL MAP>

SYMBOLIIIIIIII NAMEIIIIIII SPIIIIIIIIIIII TI TIII TEMPI TERM

REFERENCES

I TIHI TITLI TITLEI TMAXI TOPII TOTI TPI TP1I TRYY

: I:T I:Y I:P I:E

SUB-PROGRAM

:D: : I:E: : I:F:U:T I:I:S:Y I SUB-:N:E:P I PROGRAM:E:D:E I

:

SQORT :RS

STITLESDSURF

TTERH1 :RS

TYPE

TYSVTYTMP

III TTERM2I TYIIIIIIII

: I:IS I: I: I: I: I

II

: I:CS I:RS I:RS I: I:RS I:IA I: I: I:RS I:RS I:CS I:BA I:CS I:IS I:RS I:RS I:RS I:RS I:RS I

III

:RS I:RA I: I: I: I:IS I: I:RA I:RS I: I

•JSER1NINSUMMICRETERAHPPBUCKLNGBUCKLNG

USERINRAMPMICRETEINSUMRAMPUSERINCONTRLBUCKLNGMICRETEBJNOTMAINCONTRLUSERINGEOMTRYCOEFSMMPYPOWERPOWEROUTSOLUINSUMMICRETE

MICRETEGEOMTRYINSUMOUTSOLUSUBSTITRODMAPSURFLUXSUBSTITUSERIN

: : : I:X:X:C I: :X:C I: :X:C I-• :X:C I: :X:C I:X:X: I: : : I: : : I:X:X:C IsX:X: I: : :C I: :X:C I:X:X: I: :X:C I! :X:C I: :X:C I:X:X::X:X::X:X:C:X:X:lX:X:C:X:X::X:X::X:X::X:X::X:X:: : :C: :X:C:X:X:

G20MTRYRODMAPCOEFSOUTSOLUSUBSTIT

INSUMRAMPPSUBSTITOUTSOLURAMPPGEOMTRYMICRETESUBSTIT

IIIIIIIIIIIII

: : : I:X:Xi I: : :C I: :X:C: :X:C:X:X:C:X:X::X:X::X:X::X: :S

INSUHOUTSOLUINSUM

SUBSTITMICRETE

BUCKLNGRODMAPSURFLUX

MICRETEPOWER

:D: : I:E: : IF:U:T II:S:Y IN:E:P IE:D:E ID: : I: : I

SUB-PROGRAM

III1

:O: : IE: : IF:U:T II:S:Y IN:E:P IE:D:E ID: : I: : I

:X:C:X:C:X:C:X:C:X:C

:X:CX:X:: :C:X:C

X:X:X:X:C:X:C:X:C

X:X:CX:X::X:C

: :C:X:C

: :C:X:C:X:C

X:X:X:X:

REGULARCONTRLRAMPSURFLUX

USERIN

INSUMSURFLUX

USERIN

USERINMICRETEPOWER

OUTSOLUCOEFS

DEFINITION

: : I:X:C I:X:C I:X:C I:X:C I: : I: : I: : I: : I: : I: : I

X:X:C I: : I: : I:X:C I:X:C I: : I: : I: : I: : I: : I: :. I: : I: : I: : I: : I: : I

X:X:C I: : I: : I: : I: : I

X:X:C I:X:C I:X:C I: : I

X:X: I:X:P I: : I: : I: : I

SYMMETRY PARAMETER

MATERIAL BUCKLING CALCULATION DISCRIMINANT. IFDISCRIMINANT IS LESS THAN 0, THE MATERIAL BUCKLINGIS COMPLEXPROBLEM SUBTITLETEMPORARY VARIABLESURFACE FLUX CALCULATION SWITCH (1=ON, 0=OFF)

REFLECTOR COEFFICIENT T, REFERENCE 2, PAGE 26ROD SITE BESSEL FUNCTION CALCULATION SWITCH(1 - CALCULATION IS NECESSARY, 0 - NOT NECESSARY)

TEMPORARY VARIABLETERM IN JO BESSEL FUNCTION APPROXIMATIONCURRENT TIME, HH:MM:SSTABLE OF ITERATION PARAMETER NAMESPROBLEM TITLEMAXIMUM NUMBER OF LATTICE PITCHES BETWEEN ROD SITES2*PITEMPORARY VARIABLETOTAL POWERREFERENCE TOTAL POWERINTERSTITIAL FACTOR FOR A TYPICAL ROD

AR*FTERM + JAY*IKF(M)*IIK(I) + JAYP*IKF2(M)*IIK2(I)*ABCEYE*IIK(I)*IIK(M) + EYEP*IIK2(I)*IIK2(M)*ABCROD TYPE

ROD TYPE

TEMPORARY VARIABLETEMPORARY VARIABLE

01

cn <D3tx0h-*

301

•v

1u>,f5O3rr

1

NJ

<SYMBOL MAP>

I SYMBOLIIIIII NAMEIIIIIII TlI T3I T4I 0IIIIIIIIIII WII X

av

vVALUEVI

w

I XXBES

XIxtmXPTS

xs

XSEC

XTYPI XXI XXI XII 11 YII YYI

REFERENCES

SUB-PROGRAM

:D: : I:E: : I:F:U:T I:I:S:Y I:N:E:P I:E:D:E I:D: : I: : : I

:D: : I:E: : I:F:U:T I

SUB- :I:S:Y IPROGRAM :N:E:P I

:E:D:E I:D: : I

U:TSUB-PROGRAM

: I:RS I:RS I:RS I:IS I: I:RS I:IS I: I:RS I:RS I:RS I:RS I:RS I: I:RS I:RA I:RS I:RS I:RS I

I

:RS I:RS I:RS I: I:RS I:RS

COEFSCOEFSCOEFSGEOMTRY

RAMPGEOMTRY

RAMPUSERINMICRETERAMPCONTRLDETERMICRETEUSERINLINEQNIKBESSUSERIN

MICRETEPOWERUSERIN

EXX2USERIN

:X:X::X:X::X:X::X:X:: : ::X:X::X:X:: : ::X:X::X:X::X:X::X:X::X:X:C: 1X1P:X:X::X:X::X:X:: :X:P:X: :S

:X:X::X:X::X: :S

I: I:RS I USERIN: I:IS I:RS I:RS I:RS I:RS I:IS I

:X:X::X: :S

GEOMTRYMICRETEIKBESSEXX2MICRETEGEOMTRY

:X: :S

:X:X::X:X::X:X::X:X::X:X::X:X:

I : : :I : : :I : : :I : : :I MICRETE :X:X:I : : :I RAMPP :X:X:I MICRETE :X:X:I : : :I RAMPP :X:X:I : : :IIIIIIIIIIIIIIIIIIIIIIIIII

RAMPPMICRETE

PSMBJNOT

IKBESS :X:X:

IIIIIIIIII

: : : I: : : I:X:X: I: :X:C Is i : I: : : I

IIIIIIIIIIIIIIIIIIIII

!X:P:X:P

MATRIX

Y IP IE III

DEFINITION

TEMPORARY VARIABLETEMPORARY VARIABLETEMPORARY VARIABLEROD-I COORDINATE POSITION RELATIVE ROD-J COORDINATEPOSITIONREFLECTOR COEFFICIENT U, REFERENCE 2, PAGE 26ROD-I ORDINATE POSITION RELATIVE ROD-J ORDINATEPOSITIONREFLECTOR COEFFICIENT V, REFERENCE 2, PAGE 26USER PROBLEM MODIFICATION DATAIF L=0, VI=M; OTHERWISE VI=K10*KKF (L) + K11*KK(L)REFLECTOR COEFFICIENT W, REFERENCE 2, PAGE 26ESTIMATE OF PROBLEM EIGENVALUE

IF L=0, WI=i-Ll; OTHERWISE WI=K7*KK(L)TEMPORARY VARIABLETEMPORARY VARIABLEBESSEL FUNCTION ARGUMENTRESERVED NAME TO BE USED IN FUTURE VERSION OPMICRETEIF L=0, XI=QU*P10; OTHERWISE XI=-K9*KK(L)

RESERVED NAME TO BE USED IN FUTURE VERSION OFMICRETE

RESERVED NAME TO BE USED IN FUTURE VERSION OfMICRETERESERVED NAME TO BE USED IN FUTURE VERSION OFMICRETETEMPORARY VARIABLETEMPORARY VARIABLETEMPORARY VARIABLETEMPORARY VARIABLEIF L=0, YI=P3; OTHERWISE YI=P2*P4*KKF(L)TEMPORARY VARIABLE

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Appendix BProgram Source

I

ISSN 0067 - 0367

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