AFCL-7679 ATOMIC ENERGY Vs33 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
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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
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
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
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 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.
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.
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
Figure 3-2 (cont'd)Output from Typical Job
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
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
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)
DESCRIPTIVE TITLE — VOLUME 0
DETERMINATION OF LATTICE PARAMETERS USING FEW RODS (AECL-2C93)CANDU FUEL
LATTICE DESCRIPTION AND CALCULATION CONTROL DATA — VOLUME 1
LATTICE DATA — RECORD 1
INTERSTITIAL FACTOR FOR TYPICAL ROD, TRYYREFERENCE LATTICE BUCKLING, BCEALTERNATE SLOWING DOWN SOURCE (1=OHITTED), BAASURFACE FLUX CALCULATION SWITCH (1=ON), SURF
GEOMETRIC DATA — RECORD 2
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 CONTROL DATA — RECORD 3
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
MODERATOR PROPERTIES — RECORD 4
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
a) Reference lattice calculation
ROD AND CELL PROPERTY DATA — VOLUME 2
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
ABSORBED (USED ONLY WHEN POWERS ARE COMPUTED)
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
LATTICE MAP CONSISTING OF 121 RODS
-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
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
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
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
b) Substituted lattice calculation++•++++++++++++++++++++++++++++++ HICRETE - VERSION 4.1 ++ (1982 MAY 15) +
SUBSTITUTION MICRETE
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)
DESCRIPTIVE TITLE — VOLUME 0
DETERMINATION OF LATTICE PARAMETERS USING FEW RODS (AECL-2593)19 UO2 FUEL WITH HB40 ORGANIC COOLANT
LATTICE DESCRIPTION AND CALCULATION CONTROL DATA -- VOLUME 1
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 CONTROL DATA — RECORD 3
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
MODERATOR PROPERTIES — RECORD 4
FAST DIFFUSION COEFFICIENT, DFTHERMAL DIFFUSION COEFFICIENT, DSLOWING DOWN AREA, LSSQMTYPICAL CELL SLOWING DOWN AREA, LSSOCMODERATOR DIFFUSION AREA, LSQM
REFLECTOR PROPERTIES — RECORD 5
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
REFLECTOR OUTER BOUNDARY CONDITIONS AND BUCKLING CALCULATION CONTROL DATA — RECORD 6
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
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
b) Substituted lattice calculation
ROD AND CELL PROPERTY DATA — VOLUME 2
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
ABSORBED (USED ONLY WHEN POWERS ARE COMPUTED)
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
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
3 - 1 8
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
c) Test lattice calculation
HICRETE - VERSION 4.1(1982 MAY 15)
SUBSTITUTION MICRETE
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)
DESCRIPTIVE TITLE — VOLUME 0
DETERMINATION OF LATTICE PARAMETERS USING PEW RODS (AECL-2593)19 UO2 FUEL WITH HB40 ORGANIC COOLANT
LATTICE DESCRIPTION AMD CALCULATION CONTROL DATA — VOLUME 1
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
MODERATOR PROPERTIES — RECORD 4
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
REFLECTOR OUTER BOUNDARY CONDITIONS AND BUCKLING CALCULATION CONTROL DATA — RECORD 6
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
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
c) Test lattice calculation
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
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
MODERATOR PROPERTIES — RECORD 4
FAST DIFFUSION COEFFICIENT, DFTHERMAL DIFFUSION COEFFICIENT, DSLOWING DOWN AREA, LSSQMTYPICAL CELL SLOWING DOWN AREA, LSSQCMODERATOR DIFFUSION AREA, LSQM
REFLECTOR PROPERTIES — RECORD 5
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
REFLECTOR OUTER BOUNDARY CONDITIONS AND BUCKLING CALCULATION CONTROL DATA — RECORD 6
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
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
c) Test lattice calculation
ROD AND CELL PROPERTY DATA — VOLUME 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
ABSORBED (USED ONLY WHEN POWERS ARE COMPUTED)
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
NO - ROD NUMBERRHO - RELATIVE THERMAL FLUXAll - RELATIVE THERMAL ABSORPTIONS/UNIT LENGTHRHOSF - RELATIVE THERMAL FLUX ON CELL SURFACE
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.
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
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
ROD EQUIVALENT RADIUS, CM, ASSOCIATED WITH THERMALABSORPTIONS, REFERENCE 2, PAGE 11TEMPORARY VARIABLE'A' FACTOR ASSOCIATED WITH NORMAL SLOWING-DOWN OFFISSION NEUTRONS, REFERENCE 2, PAGE 5, EQUATION 5'A' FACTOR ASSOCIATED WITH NORMAL SLOWING-DOWN OFFISSION NEUTRONS, REFERENCE 2, PAGE 5, EQUATION 5ROD RADIUS, CMCOS/SIN FACTOR, REFERENCE 2, PAGE 18, EQUATIONSA AND BRATIO OF AVERAGE TO THERMAL FLUX FOR ROD OFRADIUS 'A' CM, REFERENCE 2, PAGE 11, EQUATION 20RELATIVE THERMAL ABSORPTIONS/UNIT LENGTH OF ROD
C I ALTERNATIVE SLOWING-DOWN (REFERENCE 2, PAGE 9)I CALCULATION SWITCH (1 - CALCULATION OMITTED,I OTHERWISE CALCULATION IS PERFORMED)I TEMPORARY VARIABLE
C I REFERENCE LATTICE BUCKLING, M**(-2), SUBSTITUTIONI CALCULATION ONLYI TEMPORARY VARIABLEI TEMPORARY VARIABLEI TEMPORARY VARIABLEI MODERATOR/REFLECTOR BOUNDARY CONDITION COEFFICIENTI BETA-DOUBLE-PRIME, REFERENCE 2, PAGE IS,I EQUATION 31I MODERATOR/REFLECTOR BOUNDARY CONDITION COEFFICIENTI BETA-PRIME, REFERENCE 2, PAGE 15, EQUATION 31I TEMPORARY VARIABLEI POINT VALUE OF JO BESSEL FUNCTION
C I B/A, REFERENCE 2, PAGE 23, EQUATION 41, WHERE BI IS A CONSTANT ASSOCIATED WITH THE ALTERNATIVEI SLOWING DOWN PROCESS, REFERENCE 2, PAGE 9, ANDI A IS A CONSTANT ASSOCIATED WITH THE NORMAL- SLOW-I ING DOWN PROCESS, REFERENCE 2, PAGE 5I B/A, REFERENCE 2, PAGE 23, EQUATION 41, WHERE BI IS A CONSTANT ASSOCIATED WITH THE ALTERNATIVEI SLOWING DOWN PROCESS, REFERENCE 2, PAGE 9, ANDI A IS A CONSTANT ASSOCIATED WITH THE NORMAL SLOW-I ING DOWN PROCESS, REFERENCE 2, PAGE 5I B**2
C I JO, JO+IO OR MATERIAL BUCKLING, M**(-2), ASC I COMPUTED IN SUBROUTINE BUCKLNG
II SQUARE ROOT OF RADIAL BUCKLING, M**(-1)
P I BUCKLING CALCULATION SWITCH (JO - COMPUTEI JO BUCKLING, JO+IO - COMPUTE JO+IO BUCKLING,I MATERIAL - COMPUTE MATERIAL BUCKLING, ALL -I COMPUTE ALL TYPES OF BUCKLING)I TEMPORARY VARIABLEI TEMPORARY VARIABLEI JO BUCKLING, CM**(-2)I TEMPORARY VARIABLEI
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SYMBOL REFERENCES
IIII NAMEIIIIIII BlII CARDINGIIII CIII CNPRIIIIII
: I: I:T I:Y I SUB-:P I PROGRAM:E I: I: I
:D: ; I :D: : I:E: : I :E: : I:F:U:T I :F:U:T I:I:S:Y I SUB- :I:S:Y I SUB-:N:E-P I PROGRAM :N:E:P I PROGRAM:E:D:E I :E:D:E I
D:E:F:U:TI:SsY IN:E:P IE:D:E ID: j I
DEFINITION
CI
COKE
COSSCPR
I CPR2III CRITHTI C2I C4I DIIIIII DETIIIIIIIIIIII
DATDELTA
DETER
DFOD
:RS I BJNOT :X:X:: I : : ::CS I MAIN: I REGULAR:RA
ROD EQUIVALENT RADIUS, B, TIMES ROD INTERSTITIALFACTOR, FUSER INPUT BUFFER
RATIO OF RESONANCE TO THERMAL ABSORPTIONS
RATIO OP RESONANCE TO THERMAL ABSORPTIONSREFERENCE CHANNEL POWER RELATIVE REFERENCE AVERAGECHANNEL POWER OF FLATTENED REGION (REGION CONSISTINGOF TYPE 1 FUEL)TEST LATTICE CALCULATION FLAG, SUBSTITUTIONCALCULATION ONLYROD POSITION DIRECTION COSINECHANNEL POWER RELATIVE REFERENCE CHANNEL POWERCHANNEL POWER RELATIVE REFERENCE AVERAGE CHANNELOF FLATTENED REGION (REGION CONSISTING OF TYPE 1FUEL)TEMPORARY VARIABLESURFACE FLUX COEFFICIENT, REFERENCE 4, PAGE 18SURFACE FLUX COEFFICIENT, REFERENCE 4, PAGE 18MODERATOR THERMAL DIFFUSION COEFFICIENT, CM
CURRENT DATE, YY/MM/DDDELTA, THE SLOWING DOWN ISOTROPY FACTOR,REFERENCE 2, PAGE 23, EQUATION 42PROBLEM MATRIX DETERMINANT AS COMPUTED INSUBROUTINE LINEQNPROBLEM MATRIX DETERMINANT AS COMPUTED INSUBROUTINE LINEQNMODERATOR FAST DIFFUSION COEFFICIENT, CM
DF/D, ^ATIO OF MODERATOR DIFFUSION COEFFICIENTS(PAST/THERMAL)REFLECTOR FAST DIFFUSION COEFFICIENT, CM
E/A, REFERENCE 2, PAGE 24, EQUATION 45, WHERE EIS A CONSTANT ASSOCIATED WITH THERMAL ABSORPTION,REFERENCE 2, PAGE 11 AND A IS A CONSTANT ASSOCIATEDWITH NORMAL SLOWING DOWN, REFERENCE 2, PAGE 5E/A, REFERENCE 2, PAGE 24, EQUATION 45,. WHERE EIS A CONSTANT ASSOCIATED WITH THERMAL ABSORPTION,REFERENCE 2, PAGE 11 AND A IS A CONSTANT ASSOCIATEDWITH NORMAL SLOWING DOWN, REFERENCE 2, PAGE 5GEOMETRY FACTOR (1 - HEXAGONAL, 0 - SQUARE)
ERROR MESSAGE OUTPUT BUFFERERROR NUMBERESTIMATE OF PROBLEM EIGENVALUE
TEMPORARY VARIABLEEQUIVALENT RADIUS OF ROD USED TO MODEL THERMALABSORPTIONS, REFERENCE 2, PAGE 11, EQUATION 20AS COMPUTED IN FUNCTION BXX2REFLECTOR MONOPOLE CALCULATION I, REFERENCE 2,PAGE 27
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NAME
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I SYMBOLIIIIIIIIIIIIIIIII G2
I aIIIII HTEMPI IIIII1 III
REFERENCES
: I: I:T I:Y I:F I:E I: I: I
:D: : I:E: : I:F:U:T I:I:S:Y I
:D: : I:E: : I:F:U:T I:I:S:Y ISUB- :I:S:Y I SUB- :I:S:Y I SUB-
PROGRAM :N:E:P I PROGRAM :N:E:P I PROGRAM:E:D:E I :E:D:E I:D: : I :D: : I
:FiU:T:I:S:Y I:N:E:P I:E:D:E I:D: : I
DEFINITION
IEIFLD
I III IIKI IIK2I IIP2I U KI IKBESS1I IKFI IKF2I ILI IHAXIIII1IIII
1/(1-(K/KF)**2)RATIO OF AVERAGE TO THERMAL FLUX FOR ROD OFRADIUS 'A' CM, REFERENCE 2, PAGE 11, EQUATION 20
EXTRAPOLATED HEIGHT OF REACTOR, CM
TEMPORARY VARIABLEDO-LOOP INDEX VARIABLE AND/OR TEMPORARY VARIABLE
REFLECTOR COEFFICIENT I, REFERENCE 2, PAGE 26TEMPORARY VARIABLEUSER INPUT DATA FIELD NUMBERTEMPORARY VARIABLEII0(KBAR*R), REFERENCE 2, PAGE 20, EQUATION 38II1(KBAR*R), REFERENCE 2, PAGE 20, EQUATION 38TEMPORARY VARIABLEFIRST PASS FLAG (0 - FIRST PASS)POINT VALUE OF MODIFIED BESSEL FUNCTION AS COMPUTEDIN FUNCTION IKBESSI0(KF*R), REFERENCE 2, PAGE 20, EQUATION 37I1(KF*R), REFERENCE 2, PAGE 20, EQUATION 37TEMPORARY VARIABLENUMBER OF RODS IN SECTOR OF SYMMETRY AS DETERMINEDFROM USER INPUTITERATION PARAMETER INITIAL INCREMENT
ITERATION PARAMETER INITIAL INCREMENT SUBSTITUTIONCALCULATION ONLY
TEMPORARY VARIABLE
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I SYMBOLIIIIII NAMEII1IT ——»••iI EYEPII Fi riiI FI PAII FACTORI PAC1II PAC2IItI FAC4.1I FAC5II FAC6I1 FAC7II FAC8IIIIIIIIII FPI PRODIII PTERMI
REFERENCES
: I: I:T I:Y I:P I:E I
SUB-PROGRAM
:D: : I:E: : I:F:U:T 1:IsS:Y I
D: :
:F:U:TSUB- :I:S:X
:N:E:P I PROGRAM :N:E:P:E:D:E I :E:D:E:D: : I :D: :
ROD INTERSTITIAL FACTORREFERENCE AVERAGE CHANNEL POWER OF FLATTENED REGION(REGION CONSISTING OF TYPE 1 FUEL)
MODIFIED BESSEL FUNCTION APPROXIMATION FUNCTIONCOEFFICIENTSMODIFIED BESSEL FUNCTION APPROXIMATION FUNCTIONCOEFFICIENTSMODIFIED BESSEL FUNCTION APPROXIMATION FUNCTIONCOEFFICIENTSMODIFIED BESSEL FUNCTION APPROXIMATION FUNCTIONCOEFFICIENTSMODIFIED BESS"., FUNCTION APPROXIMATION FUNCTIONCOEFFICIENTSMODIFIED BESSEL FUNCTION APPROXIMATION FUNCTIONCOEFFICIENTSMODIFIED BESSEL FUNCTION APPROXIMATION FUNCTIONCOEFFICIENTSMODIFIED BESSEL FUNCTION APPROXIMATION FUNCTIONCOEFFICIENTSROD THERMAL UTILIZATION FACTOR
ITERATIVE CALCULATION SUCCESS/FAILURE FLAG SET INSUBROUTINE CONTRLROD FOUR FACTOR ETA
REFERENCE POWER CALCULATION SWITCH (0 - ON, 1 - OFF)ROD THERMAL UTILIZATION FACTOR
EFF*IKF(I)*IKF(M) + EFFP*IKF2(I)*IKF2(M)*ABC
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I SYMBOLI
REFERENCES
i D; s I:E: : I:F:U:T I:I:S:Y I SUB-:N:E:P I PROGRAM:E:D:E I
II
GEOMTRYCONTRLBUCKLNGGEOHTRYCONTRLBUCKLNG
:X:C:X:C:X:C:X:C:X:C:X:C
IQ1IQ2
I IQ3I IRECDI ISI ISTOIP2
ITER
:D: : I:E: : I:F:U:T I:I:S:Y I SUB-:N:E:P I PROGRAM:E:D:E I:D: : I: : : I
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
:D: ::E: :sFlUlT
SUB- :I:S:Y I:N:E:P I PROGRAM :N:E:P I:E:D:E I :E:D:E IiDs : I :D: : I
SUB-PROGRAM
I : i
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: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 »•**
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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
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
: : : 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
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
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II SYMBOLI
IIIIIIII
REFERENCES
NAME
NPTS
HSEC
NT
IIIIIIIIIIIIIIII NTYPIIIIII NlIriiiiiiI OTTOII PI PI PIIII PAI PARAMII
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
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
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
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<SYMBOL MAP>
I SYMBOLIIIIII NAMEIIIIIII TlI T3I T4I 0IIIIIIIIIII WII X
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
To identify individual documents in the series
we have assigned an AECL- number to each.
Please refer to the AECL- number when re-questing additional copies of this document
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KOJ 1J0
ISSN 0067 - 0367
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