ATOMIC ENERGY Vs33 L'ENERGIE ATOMIQUE OF CANADA LIMITED … · ATOMIC ENERGY Vs33 L'ENERGIE...
Transcript of ATOMIC ENERGY Vs33 L'ENERGIE ATOMIQUE OF CANADA LIMITED … · ATOMIC ENERGY Vs33 L'ENERGIE...
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
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
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
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
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
Figure 3-2 (cont'd)Output from Typical Job
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)
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
a) Reference lattice calculation
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
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 DATA — RECORD 1
INTERSTITIAL FACTOR FOR TYPICAL ROD, TKYYREFERENCE LATTICE BUCKLING, BCE =ALTERNATE SLOWING DOWN SOURCE (1-OMITTED), BAA =SURFACE 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 » 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
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
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
b) Substituted lattice calculation
MICRETE PROBLEM SOLUTION
RESULTS — INTERMEDIATE CALCULATIONS
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
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
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 CONTROL DATA — RECORD 3
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
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 —
RODRADF5.230001.000005.230001.000004.220001.000004.450001.000001.750001.00000
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
LATTICE MAP CONSISTING OF 121 RODS
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
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
c) Test lattice calculation
MICRETE PROBLEM SOLUTION
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
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
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
LATTICE DATA — RECORD 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
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
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
LATTICE MAP CONSISTING OF 163 RODS
-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
Figure 3-4 (cont'd)Output from Substitution Experiment Analysis Job
c) Test lattice calculation
MICRETE PROBLEM SOLUTION
RESULTS — INTERMEDIATE CALCULATIONS
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
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).
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
BUCKLNGXNSUM
BUCKLNGINSOM
: : I: : I: : I::X: I: : I: : I: :C I: :C I:X:C I: ! I: : I: : I
INSUMGEOMTRYSURFLUX
:C
X:C
IIIIIIIIIIIIII
: I: I: I:C I
:X:C I: I: I: I: I:C I
X:C I: I: I: I: I: I: I: I: Ir I:C I
X:C 1X:C I: I: I
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
RELATIVE THERMAL ABSORPTIONS/UNIT LENGTH OF RODTEMPORARY VARIABLETHERMAL FLUX BOUNDARY CONDITION (1=PERFECTREFLECTOR, 0-BLACK BOUNDARY)
MODERATOR/REFLECTOR BOUNDARY CONDITION COEFFICIENTALPHA-DOUBLE-PRIME, REFERENCE 2, PAGE 15,EQUATION 31FAST FLUX BOUNDARY CONDITION (1=PERFECT REFLECTOR,0-BLACK BOUNDARY)
MODERATOR/REFLECTOR BOUNDARY CONDITION COEFFICIENTALPHA-PRIME, REFERENCE 2, PAGE 15, EQUATION 31NON-LEAKAGE FACTOR, REFERENCE 1, PAGE 6,EQUATION 7-DFOD/(1-K»K»LFSQ)TEMPORARY VARIABLECOEFFICIENTS OF THE POLYNOMIAL BEING EVALUATEDTEMPORARY VARIABLEROD EQUIVALENT RADIUS, CM, REFERENCE 2, PAGE 4,EQUATION 4
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ROD EQUIVALENT RADIUS,FACTOR, F
B, TIMES ROD INTERSTITIAL
<SYMBOL HAP>
I SYMBOLIIIIII NAMEIIII
REFERENCES
: I: I:T I:Y I:P I:E I: I: I
SUB-PROGRAM
:D: : I:E: : I:P:O:T I:I:S:Y I:N:E:P I:E:D:E I:D: : I
:D: s I:E: : I:F:UJT I
SUB- :I:SJY IPROGRAM :N:E:P I
:E:D:E I:D: s I: : : I
SUB-PROGRAM
D:
F:U:T
BAAIIIII BBI BCEII BEEI BESSI BETAI BETADPIIIIIIIIIIIIIIIIIIII
• I
IIIII
:RS
BETAP
BGUESSBJNOTBOA
BOB
BSQBSQ
II
: I: I:RS I:RS I: I:RS I:RS I:RS I:RS I: I: I
II
• I
MICRETBIHSUM
SURFLUXMICRETBIHSUMBUCKLNGBJNOTBUCKLNGRAMP
:RS:iRS-:RS I:RA I: I: I: I
I:RS I
:RS:RS
RAMP
BUCKLNGBJNOTMICRETBPOWER
COEFS
I : :C: :X:C: : ::X:X:: : :C: :X:C:X:X::X:X::X:X:
:X:X:: : ::X:X:
:X:X!
BUCKBUCKOPT
:RS:CS
BUCK1I BUCK 2BUCK99BUFF
:RS:RS:RS I
COEFSUSERINCONTRLBUCKLNGBUCKLNGREGULAR
BUCKLNGBUCKLNGBUCKLNG
:RS I LINEQN: I
:X:X:: : :C: •. :C:y.:X:C:X:X::X:X:
:X:X::X:X::X:X::X:X:
OUTSOLUSDBSTIT
OUTSOLUSUBSTIT
RAMPP iX:X:
COEFSSURFLUX
GEOMTRYMICRETSSUBSTIT
: : I: :C I USERIN:X:C I: : I: : I: :C I USERIN:X:C 1: : I: : I: : I
I: : : I: : s I:X:Xi I: : : I: : : I: : : I:X: :C I OUTSOLU: :XiC I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : :C I INSUM: : :C I SURFLUX:X:X:C I
:X
SUBSTIT :X:X: BUCKLNG
DEFINITION
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
IIIIIIIIIIII
-IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
3
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<SYMBOL MAP>
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
:RS
MICRETEOUTSOLUOUTSOLUOUTSOLU
:X:X: I: :X:V> I: : :C I: :X:C I:X:X:
ERRORSSUBSTITCOEFSSURFLUXSURFLUXPOWER
:CS
:RA':RA
:RA
: I:RS I:RS I:RS I':RS I: I: I:CS I:RS I: I
IIIIIIII
: I:RS I: I: I: I
SUBSTIT :X:X:
HICRETEOUTSOLUOUTSOLU
REGULARSURFLUX.SURFLUXBUCKLNGMICRETERAMPPMAINCOEFS
:RS I DETER
:RS I DETER
X:X: II POWERI POWERI
I : : I: : : I: : : I:X:X:P I: :X:P I:X: :C I: :X:C:X: :S:X:X:P
X:X: IX:X: I:X:X: I: : :C I! :X:C I: :X:C I:X:X:C:X:X:
USERINCOEFSSURFLUXINSUH
LINEQN
:RS
:RS
BUCKLNGMICRETERAMPPMICRETE
CONTRLSUBSTITRAMP
: : :C I: :X:C I: :X:C I:X:X: I: : : I: iC I: :C I:X:C I: : I
USERINCOEFSSURFLUXCOEFS
MICRSTEUSERINRAMPP
USERIN
POWERIIII
: : : I: : : I: : ': I: : : I:X:X:P I:X:X:P I: : : I: : : I: : : I: : : I: : : I
II
:X:X:C: :X:C: :X:C I:X:X:C I: : : I: : : I:X:X:P I: : : I: : : I: : : I:X:X:C I: :X:C I: :X:C I:X:X: I: : : I: : :C I:X:X:C I: :X:C I: : : I
INSUMRAMP
MICRETE
INSUHRAMP
SURFLUX
BUCKLNGINSUM
:C
: : I: : I: ! I
X.-XsP I: ! I
IIIIIIIIIIIIIIIIIIIIIII
: : I: : I: ! I:X:C I:X:C I: ! IX:X; I: : I: :C I:XsC I: ! I: : I
: s:X:C:X:C
: s:X:S
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
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<SYMBOL MAP>
I SYMBOLI
IIII NAMEIIII
REFERENCES
: I: I:T I:Y I:P I:E I: I
I
• SUB-PROGRAM
•Di t I
!E: : I!F:U:T I:I:S:Y I:N:E:P I:E:D:E I:D: : I: : : I
iD: : I:E: : I:F:U:T I
SDB- :I:S:Y IPROGRAM :N:E:P I
:E:D:E I:D: : I: : : I
SUB-PROGRAM
DK
DR
EFF
REGULAR :X:X:
I EFFHSQI BPPPIIIIIIIIIIIIIIIIII
EKEPF
EOA
EOB
EPSLN
ERRDESC
:RS
:RA
CONTRLSUBSTITRAMPMICRETE
REGULARMICRETE
GEOMTRYMICRETESUBSTITMICRETESURFLUX
I ERROREST
EXX1EXX2
EYE
: I:RA I: I: I:RS I: I: I
II
:RS I:RS I: I:RS I: I: I
IIIIII
: I• I:RS I: I: I: I: I:CS I:IS I:RS I: I: I:RS I:RS I: I: I
:RS I MICRETE: I: I
: :C: :C:X:C
:RS I COEFS :X:X:
USERINCONTRLRAMPPRODMAPSORFLOXERRORSERRORSGEOMTRYMICRETESUBSTITEXX2EXX2
:X: :C: : :C: iC
: :X:C: :X:C:X:X:: :X:P: : :C: : :C: : :C:X:X::X:X:
MICRETEUSERINRAMPP
REGULAROUTSOLUUSERINCOEFSPOWER
: : :C:X:X:C: :X:C
: : :C: : :C:X:X:C:X: :CI : --C
REGULARCOEFSSUBSTITMICRETEBUCKLNG
REGULAROUTSOLUUSERIN
: :C: :C: :C:X:C:X:C
: : :C: : :C:X:X:C
RAMP :X:X:
IIIII BUCKLNGi INSUMIIIIIIIIIIIIIIIIIIIIIIIIIIII1II1II
CONTRLBUCKLNGINSUMOUTSOLU
INSUMRAMPGEOMTRYOUTSOLU
INSUMBUCKLNGCONTRL
RAMPP
0:E:F:U:TI:S:Y IN:E:P IE:D:E ID: : I: : I
DEFINITION
: :C:X:C
IIIIII
: : I: : I: : I: : I: : I: : I: :C I: :C I:X:C I: :C I: : I: : I: : I: : I: : I
IIIIII
: : I: : I: : I: :C I: :C I:X:C I: : I: : I: : I: : I
X:X: I: : I: : I
: :C: :C:X:C:X:C
DELTA-K, CHANGE IN K-EFFECTIVE, MK, COMPUTEDDURING LEVEL COEFFICIENT OF REACTIVITY CAL-CULATION, REGULAR MICRETE CALCULATION ONLYREFLECTOR THERMAL DIFFUSION COEFFICIENT, CM
REFLECTOR MONOPOLE CALCULATION F, REFERENCE 2,PAGE 27EFFECTIVE MIGRATION AREA, CM**2REFLECTOR DIPOLE CALCULATION F*, REFERENCE 2,•>AGE 27K-EFFECTIVE
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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<SYMBOL MAP>
NAME
GAMGNOT
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
INC
INCS
INCSV
: I:RS I:RA I: I: I:RS I:RS I: I: I: I: I:RS I:IS I: I: I: I: I:RS I
:RA:RA:IS I:IS I:RS I: I:RA I:RA I:IS I:IS I: I:RS I: I: I:RS I: I: I:RS I: I
COEFSCONTRLPOWERUSERINCOEFSGEOMTRYRAMPPUSERINCONTRLBUCKLNGREGULARUSERININSUMMMPYOUTSOLUSUBSTITSAMPUSERINUSERINMICRETEMICRETEMICRETEBUCKLNGCONTRLIKBESS
MICRETEMICRETERODMAPUSERIN
USERININSUMOUTSOLUUSERININSUMOUTSOLUREGULAR
: : :C: : :C:X:X:C:X:X:: : :C: : :C:X:X:C:X:X:C: :X:C:X:X::X:X:
:X:X:P: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: :X:C: :X:C:X:X:C: :X:C: :X:C:X:X:
IIIIIII RODMAP
SURFLOXMICRETEBUCKLNGINSUM
OUTSOLUREGULARMICRETESUBSTITSUBSTITGEOMTRYRODMAPMATRIXSURFLUXIKBESSRAMPP
:X:X:: : :C: : :C: :X:C: : :: : :C: : :C:X:X:C: :X:C:X:X:C:X:X:
SURFLUXSUBSTIT
RAMPSURFLUXINSUMCOEFS
REGULARI MICRETE
:X:X::X:X:P
LINEQN :X:X:
INSUM :X:X:
GEOMTRYCONTRLBUCKLNGGEOMTRYCONTRLBUCKLNGSUBSTIT
: :X:C:X:X:C: :X:C: :X:C: :X:C: :X:C:X:X:
LINEQNBUCKLNGCONTRL
:X:X::X:X::X:X::X:X:
REGULARMICRETESUBSTITREGULARMICRETESUBSTIT
: : I: : I: :C I: :C I: : I: : I: :C I: :C I:X:C I:X:C I: : I: : I
IIII
: •. .: I: : : I: : : 1: : : I: : ! I: : : Is : : I: : i I: : : I! : : I: : : I: : : I: : : I! : : I: : : I:X:X:C I: :X:C I:X:X:C I: :X:C I: :X:C I: :X:C I: : : I: : : I
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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<SYMBOL MAP>
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: :
SUB-PROGRAM
III-III
•:U:T I::S:Y II:E:P I
:E:D:E I:D: : I
I
FAC3
FF
FLAG
FN
: I:RS I: I:RS I:RA I: I: I:RS I:RS I: I:RS I:RA I: I:RA I:- I:RA I: I:RA
:RA
:RA
IRA
:RA
:RA:::CSsRA
:RS:RA
:RS
MICRETE
LINEQNPOWERUSERINMICRETERAMPPOWER
SUBSTITIKBESS
IKBESS
IK3BSS
:X:1II
:X:X: I: : :C I:X:X:C I: :X:C I:X:X:P I:X:X:
BUCKLNGINSUMSURFLUXRAMPP
:X:X::X:X:
:X:X:: : ::X:X:
IKBESS :X:X:
IKBESS
IKBESS
IKBESS
IKBESS
CONTRLBUCKLNGIHSOMREGULAR
CONTRLBUCKLNGINSUMPOWERCONTRLBUCKLNGINSUMHICRETE
:X:X:: : ::X:X:
:X:X:: : ::X:X:
: : :C: : :C: :X:C I
: : : I: : :C I: : :C I: :X:C:X:X:: : :C: : iC I: :X:C I:X:X:
MICRETESUBSTITPOWERSUBSTIT
MICRETESUBSTITPOWER
MICRETESUBSTITPOWER
: : : I: : : I: : : I: : : I: : :C I: :X:C I: :X:C I.•X.-X.-P I! : : I: : : I: : : I: : : I: : .: I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : : I: : :C I: : :C I: :X:C I: :X: I: : : I: : :C I: : :C I: :XsC I.- : i I: : :C I: : :C I: :X:C I: : : I: : : I
SUBSTITCONTRL
SURFLUXUSERIN
CONTRL
SURFLUXUSERIN
SURFLUXUSERIN
DEFINITION
: I: : I: : I: : I: :C I:X:C I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: :C I
X:X:C I: : I
X:X:P I: : I: :C I
X:X:C I: : I: : Is :C I
X:X:C I
: :
REFLECTOR DIPOLE CALCULATION I*, REFERENCE 2,PAGE 27ROD INTERSTITIAL FACTORROD INTERSTITIAL FACTOR
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
-30)CT
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<: SYMBOL MAP>
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
D:
IIIII
E: : IF:U:T I:S:Y I
N:E:P IE:D:E ID: : I: : I
REGULARHICRETESUBSTITREGULARMICRETESUBSTIT
RAMPUSERIN
RAMPUSERIN
RAMPUSERIN
CONTRLUSERINSUBSTITREGULAR
DEFINITION
: : I:X:C I:X:C I:X:C I:X:C I:X:C I:X:C I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: : I: :C I
X:X:C I: : I: :C I
X:X:C I: : I: :C I
X:X:C I: : I: : I: : I: : I: : I: : I: : I: :C I
X:X:C I:X:C I: :C I: : I
ITERATION PARAMETER INITIAL INCREMENT SMALL CORETEST LATTICE SUBSTITUTION CALCULATION ONLY
ITERATION PARAMETER INITIAL INCREMENT LARGE CORETEST LATTICE SUBSTITUTION CALCULATION ONLY
MATRIX PROBLEM CALCULATION SWITCH (1 - SOLVEPROBLEM, 2 - COMPUTE MATRIX DETERMINANT)TEMPORARY VARIABLEI0(K*A)I0(KBAR*A)
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
CDXTI-1
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< SYMBOL MAP>
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
: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
< I IiXtXl<XiX:iXcXiC: tXiCtil
RAMPPRAMP
SURFLUX iXtXlPSH : :X:
I NIC8BTE i <X:I LIHBQH >XlX:IIIIIIIIIIII
XHSDKGMMTRYMATRIXSORFLOX
I RIGOLARILINEQNCOIFS
tXtXlPtXiX:t ) tt s *: s it i :t : :
:X:C: :C
:Cs ;CiX:C
: t:
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 !
OUTSOLUCONTRL
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
:•
:T:Y:P:E
:
:
:RS::RS::RS:RS:RS:RA:::RA:IS:RA:RA:IS:RS:RS:RS:RS:RS:RA;::RArRS:RS:RS:RS:RS:RS:RS:RS::RS:RA::R *::RA
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
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
:•D: :B: ::P:OsT
SOB- :PROGRAM :
:
RAMPP :
CONTRL !POWER
CONTRLPOWER
OOTSOLO
OOTSOLO
OOTSOLO
OOTSOLO
I:S:YN:E:PE:D:ED: :
•• s
: .
:X:C: :: •• ;: :; ;: ;
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: : :: i :: :X:C: : :: : :: :X:C: : :: :X:C: : :: :X:C: : :
IIIT
IIIIIIII
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
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
:U:T:Y
:E:P:D:E
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
-3
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2 OCJ O
rT
<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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cren
Scro3 o0) O
V 3
(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
en a>3 >cr io uioo3(T
«.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
III- I — .-.—.._.
:E
:D: : I:E: : I:F:U:T I:I:S:Y I:N:E:P I:E:D:E I:D: : I: : : I
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 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;••
.
•
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• ;
: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• ;
X:X:
. i
: :C: :C
)::X:C• ::X:C:X:C: i
. ;
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: : iCt : :: : :C
: : :: : :
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
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I
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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
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I: I:RS I USERIN: I:IS I:RS I:RS I:RS I:RS I:IS I
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GEOMTRYMICRETEIKBESSEXX2MICRETEGEOMTRY
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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
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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
IIIIIIIIIIII
-IIIIIIIIIII
IIIIIIIIIIIIIIIIIIIII
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