ML20126A394

Forwards Four Documents Listed by Board in 921002 Memorandum Re Board Questions

ML20126A394
Person / Time
Site:	Millstone
Issue date:	10/20/1992
From:	Hodgdon A NRC OFFICE OF THE GENERAL COUNSEL (OGC)
To:	Kelber C, Kline J, Smith I Atomic Safety and Licensing Board Panel
References
CON-#492-13469 OLA, NUDOCS 9212210033
Download: ML20126A394 (801)

Text

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'# '. UNITED STATES

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NUCLEAR REGULATORY COMMISSION 7, E WASHING TON, D. C. 20$55

' 72 DEC 16; PS:50 October 20,.1992 Ivan W.. Smith, Chairman CharlesN.KelbebcNMGhb$[

Adr e.nistrative Judge ERANo!

AtomicLSafety_and Licensing Board Atomic Safety and Licensing U.S._ Nuclear Regulatory Board Commission- U.S. Nuclaar Regulatory Washington, DC 20555- Commist, ion Washington, DC 20555 Jerry R. Kline Administrative Judge Atomic Safety and Licensing Board ,

U.S. Nuclear Regulatory commission Washington, DC 20555 In the Matter of NORTHEAST NUCLEAR ENERGY COMPANY Docket No.(s) 50-336-OLA flillistone: Nuclear Power Station. Unit No. 2)

Dear Administrativa Judges:

Enclosed herewith-please find copies of the four_ documents listed by the Licensing Board in its Memorandum (Regarding Board' Questions) dated-October 2, 1992.

A c CW Ann P. Hodgdon-Counsel for NRC Staff-

Enclosures:

:As stated cc w/encls.: Service List- ,

-EESIGNATED ORIGIN 1D' er 9212210033 921020 O<}t PDR ADOCK 05000336 '

U^ ~ ' ' t "'I ?V _ _J _h }Ms

.O PDR S07-

,1 JNS TRANSAn It OFTHE AMERICAN NUCLEAR SOCIETY ,

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i_ Volume 64 November 10-14, 1991 San Francisco Hilton Hotel TANSAO 641-754 (1991)-

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San Francisco, California ISSN: 0003-018X Edward L. Quinn (MDM)

Technical Program Chair Eric A. Blocher (Gilbert / Commonwealth)

! Robert W. Hess (PG&E)

!{ Assis: ant Technical Program Chairs l3l1

L W

Irene O. Macke (ANS)

~

Edstor Ellen M. Burke (ANS)

Coordinator ,

NOTICE TO READER: A COPY OF THIS EIGHT PAGE DOCUMENT-IS RETAINED IN THE OFFICIAL

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DOCKET FILE OF THIS PROCEEDING (50-336-OLA).

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Emile L. Juli Chief N Docketing and Service Branch Office of the secretary of the Commissio COPYRIGHT C 1991 AMERIC AN NUCLE AR SOCIETY. INCORPOR ATED,I-Printed in US A

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I NUREG/CR-0200 Volume 2. Section F11 ORNL/NUREG/CSD-2/Vl/R2 COMPUTING AND TELECOMMUNICATIONS DIVISION at  :

Oak Ridge National J.aboratory >

Post Office Box X Oak Ridge, Tennessee 37830 KENO V.a AN IMPROVED MONTE CARLO CRITICALITY PROGRAM WITII SUPERGROUPING L M. Petrie N. F. Landers Manuscript Completed: March 1983 Date Published: December 1984 Prepared for the Office of Nuclear Material Safety and Safeguards U. S. Nuclear Regulatory Commission Washington, DC 20555 Under interagency Agreement DOE 40-549-75 NRC FIN No. B-0009 Martin Marietta Energy Systems,Inc.

operating the Oak Ridge National Laboratory Oak Ridge Y-12 Plant Oak Ridge Gaseous Diffusion Plant Paducah Gaseous Diffusion Plant under Contract No. DE-AC05-840R21400 for the DEPARTMENT OF ENERGY i

4

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CONTENTS LIST OF FIGURES - . Fi l.vii."

Fil.xiii LIST OF TABLES ACKNOWLEDGMENTS . Fil.xix AUSTRACT Fil.xxi Fi l.1 INTRODUCTION TO KENO V.a ' Fi l.l.1 Fil.2 TilEORY AND TECilNIQUES Fi l.2.1 Fi l.2.1 Tile TRANSPORT EQUATION Fi l.2.1 F i l.2.2 COLLISION TREATMENT F11.2.5 F i l .2. 3 BIASING OR WEIGitTING Fi l.2.6

• Fi1.2.4 DIFFERENTIAL ALBEDOS Fl1.2.9 F i l .2.5 SUPERGROUPING Fi l .2.9 F i l .2.6 RESTART Fi l.2.10 F i l .2.7 GEOMETRY Fi l .2. l l -

F11.

2.8 REFERENCES

F11.2.1 i Fil.3 LOGICAL PROGRAM FLOW Fi l .3.1.

Fi l .3.1 PROGRAM INITIATION Fi l.3.1 Fil.3.2 PARAMETER DATA Fi l.3.2 Fi l .3.3 OVERALL PROGRAM FLOW Fi l.3.4 Fi1.3.4 PROliLEM DESCRIPTION Fi 1.3.6 Fi l .3.4.1 Array Data Fi l.3.9 Fi l .3.4.2 Geometry Data . Fi l.3.10 Fi l.3.4.3 Mixing Table Data Fil.3.12 l' Fi l .3.4.4 Plot Data . . Fi l.3.13 Fi l .3.4.5 Biasing Data , Fil.3.14 F11.3.4.6 Restart Data . FI 1.3.15 Fi l.3.4.7 Generate Remaining Data . Fi l.3.16 Fi l .3.5 CREATE A MIXED CROSS SECTION DATA FILE , ,

Fi l,3.18 l

F I l .3.5.1 Cross.Section Mixing . . F11.3.20.

F11.3.5.2 Generate Angles and Probabilitics . Fi 1.3.21 i-Fi l.3.6 WRITE CROSS SECTIONS ON DIRECT ACCESS FILE , . . Fil.3.22

! Fil.3.7 WRITE INPUT DATA ON RESTART FILE , Fi l.3.23 l

Fl1.3.8 GENERATE ALBEDO CROSS SECTION CORRESPONDENCE TABLES Fi l.3.24 Fi1.3.9 GENERATE SUPERGROUPED D i A . Fi 1.3.25 Fi 1.3.9.1 Print Macroscopic Cross Sections . F11.3.27 -

Fi l.3.9.2 Write Supergroup Data File F11.3.28 i

Fi 1.iii

Fi1.3.10 PROCESS GEOMETRY . . F11.3.29 -

Fi l .3.10.1 Load Data From the Direct Access File Fi l .3.31 -

Fi l .3.10.2 Check the Geometry Data , . Fi l.3.33 Fi l .3.10.2.1 Determine Distances Fil.3.35 -

Fi 1.3.10.3 Calculate Volumes ~ F11.3.36 -

Fil.3.11 LOAD BI ASING OR WElGHTING DATA Fil.3.37 Fil.3.12 GENERATE PRINTER PLOT - Fil308 -

Fl!.3.13 PROCESS HISTORIES BY SUPERGROUP FilJ.39 Fi l .3.13.1 Load Calculated Restart Data . Fi l.3.42 F i l .3.13.2 Generate Initial Source Distribution- Fi l.3.43 F i l.3.13.3 Track Individual Histories Fi l.3.46 Fil.3.13.4 - Provide the Next Generation Source Fil.3.54 -

F11.3.13.5 End of Generation Processing Fil.3.55 F11.3.14 END OF PROBLEM PROCESSING - Fil.3.56 Fi1.3.15 PRINT FLUXES Fil.3.57 Fil.3.16 REFERENCES . . Fi l.3.58 Fil.4 KENO V DATA GUIDE . . Fi l.4.1 '

Fi1.4.1 KENO V INPUT OUTLINE . , . . F11.4.1 Fi l .4.2 PROCEDURE FOR DATA INPUT Fi l .4.3 Fi l .4.3 TITLE AND PARAMETER DATA Fi l .4.4 F11.4.4 GEOMETRY DATA . Fi1.4.8 Fi l .4.5 ARRAY DATA . . Fi l.4.19 -

Fi1.4.6 ALBEDO DATA , , F11.4.26 Fi l.4.7 BIASING OR WEIGHTING DATA . . . Fil.4.29 Fil.4.8 START DATA - . . . . Fi l.4.32 Fi l .4.9 EXTRA 1-D XSECS ID'S DATA . . Fil.4.35 F11.4.10 MIXING TABLE DATA FI 1.4.36 F11.4.1I PLOT DATA , . F11.4.37 Fil.4.12 REFERENCE. . . . . Fil.4.41.'

Fil.5 NOTES FOR KENO V USERS . . . . Fi l.5.1

. Fil.5.1 -DATA ENTRY Fl !.5.1 -

F11.5.2 DEFAULT LOGICAL UNIT NUMBERS FOR KENO V. Fil.5.2 -

Fil.5.3 PARAMETER INPUT . . . Fi l.5.3 .

Fi l.iv 1v-~ -

1rw rw- e- , ., a, , --y e- n --

4ese .- .-~~v.a wm, , ,, . , , - , -,a. a w- a ,*~en va-e-e ~

a F i l,5.4 CROSS SECTIONS Fil.M.3 Fil.5.4.1 Use a Premixed Cross-Section Data File. Fi l.5.3 Fi 1.5.4.2 Use an AMPX Working Library Fi1.5.4 Fil.5.4.3 Number of Scattering Angles . Fil.5,4 F 11.5.4.4 Cross-Section Message Cutoff 11.5.4 Fil.5.5 . MIXING TABLE ,

Fi l.5.5 =

- Fl!.5 6 GEOM ETRY Fil.5.6-Fil.5.6.1 Use of Holes in the Geometry Fi l.5.23 F11.5.6.2 Nesting Holes Fi 1.5.29 Fi 1.5.6.3 Multiple Arrays F11.5.39 ,

Fi1.5.6.4 Arrays and Holes Fl 1.5.49 Fil.5.6.5 Specification of the Global System Fi l.5.63 Fil.5.7 ALTERNATIVE SAMPLE PROBLEM MOCK-UPS Fi l.5.69 F i l .5.7.1 Sample Problem 12, First Alternative Fi l.5.69 Fil.5.7.2 Sample Problem 12, Second Alternative Fi l.5.71 Fi l .5.7.3 Sample Problem 13, Alternative Fi l.5.72 Fil.5.8 BIASING OR WEIGHTING DATA ,

Fi l.5.73 FI 1.5.9 PRINTER PLOTS ,

. F11.5.75 Fil.5.10 RESTART CAPABILITIES Fi l.5.109 Fil.5.li RANDOM SEQUENCE - Fi l.5.I l0 Fil.5.12 MATRIX K-EFFECTIVE Fi l.5.120 Fil.5.13 DEVIATIONS .

Fi l.5.121 Fi1.5.14 GENERATION TIME AND LIFETIME . . . F11.5.121 Fil.5.15 REFERENCE ,

Fi l.5.121 F

11.6 DESCRIPTION

OF OUTPUT . . .

F 11.6.1 F i l .6.1 HEADER PAGE . , .

Fi1.6.1 F i l .6.2 PROGRAM VERIFICATION INFORMATION ' - - Fi l .6,1 Fl 1.6.3 TABLES OF PARAMETER DATA .. . Fi1.6.2

' F11.6.4 UNPROCESSED GEOMETRY INPUT DATA - Fl 1.6.4 Fil.6.5 TABLE OF DATA SETS USED IN THE PROBLEM - Fil.6.4 Fil.6.6 MIXING TABLE DATA . .

Fi l.6.5 :

Fl1.6.7 ALBEDO CROSS SECTION CORRESPONDENCE .

Fi 1.6.6 Fi l.6.8 1-D MACROSCOPIC CROSS SECTIONS . . . . Fi l.6.7 Fil.6.9 EXTRA 1 D CROSS SECTIONS , ,

Fi l.6.8 F11.6.10 2-D MACROSCOPIC CROSS SECTIONS > .

Fi 1.6.8 FI1.6.1i PROBABILITIES AND ANGLES .. . Fl 1.6.9 Fil.6.12 TABLE OF ADDITIONAL INFORMATION - ,

Fi l.6.9 Fl1.6.13 TABLE OF SPACE AND SUPERGROUP INFORMATION - . F11.6.11

. Fil.6.14 ARRAY

SUMMARY

Fi l.6.12 Fil.6.15 GEOMETRY DATA Fi l.6.13 '

Fil.6.16 UNIT ORIENTATION DESCRIPTION Fi16.14 Fil.6.17 VOLUME INFORM ATION Fil.6.14 '

Fi l.v

Fi1,6.18 BIASING INFORMATION . . 4 Fi l.6.15 Fil.6.19 GROUP DEPENDENT WEIGilTS Fi l.6.16 F11.6.20 PICTURE OR PLOT REPRESENTATION . F11.6.16 Fil.6.21 CONCLUDE PRE TRACKING EDITS . , . . Fi l.6.18 Fl1.6.22 PRINT STARTING POINTS . Fil.6.19 Fil.6.23 K EFFECTIVES BY GENERATION Fi l.6.20 Fil.6.24 FINAL K EFFECTIVE EDIT Fi l.6.22 -

Fil.6.2$ PLOT OF AVERAGE K EFFECTIVE BY GENERATION RUN Fi l.6.23 Fil.6.26 PLOT OF AVERAGE K EFFECTIVE BY GENERATION SKIPPED Fi l.6.23 Fil.6.27 FINAL EDIT OF FISSIONS, ABSORPTIONS, AND LEAKAGE Fi l.6.24 Fil.6.28 MATRIX K-EFFECTIVE BY UNIT LOCATION Fil 6.26 Fil.6.29 FISSION PRODUCTION BY POSITION INDEX MATRIX Fi l .6.27 Fil.6.30 SOURCE VECTOR BY POSITION INDEX Fi l.6.27 Fil.6.31 COFACTOR K. EFFECTIVE BY POSITION INDEX Fi l.6.28 Fil.6.32 MATRIX K EFFECTIVE BY UNIT NUMBER Fi l.6.28 Fil.6.33 FISSION PRODUCTION BY UNIT NUMBER MATRIX FI L6.29 Fi1.6.34 SOURCE VECTOR BY UNIT NUMBER , Fl 1.6.29 ,

Fil.6.35 COFACTOR K. EFFECTIVE BY UNIT NUMBER Fi l.6.30 Fil.6.36 MATRIX K EFFECTIVE BY llOLE NUMBER Fil.o.30 -

F11.6.37 FISSION PRODUCTION BY llOLE NUMBER MATRIX F11.6.30 Fi1.6.38 SOURCE VECTOR BY liOLE NUMBER Fi 1.6.31 <

Fil.6.39 COFACTOR K-EFFECTIVE BY HOLE NUMBER Fi l.6.31 Fil.6.40 MATRIX K. EFFECTIVE BY ARRAY NUMBER Fi l.6.31 Fil.6.41 FISSION PRODUCTION BY ARRAY NUMBER MATRIX Fi l.6.32 Fil.6.42 SOURCE VECTOR BY ARRAY NUMBER , Fi l.6.32 Fil.6.43 COFACTOR K EFFECTIVE BY ARRAY NUMBER Fi l.6.32 Fil.6.44 FISSION DENSITY EDIT Fi l.6.33 Fil.6.45 FLUX EDIT F i l.6.33 F11.6.46 FREQUENCY DISTRIBUTIONS F11.6.34

='

Fil.7 WARNING MESSAGES AND ERROR MESSAGES Fi l.7.1 F11.7.I MESSAGES Fi 1.7.1 Fi1.7.2 STOP CODES . Fl 1.7.32 Fil.A ' APPENDIX A - ALPHABETICAL INDEX OF SUBROUTINES Fi l . A. I Fi 1.B APPENDIX B - ALPilABETICAL INDEX OF COMMONS Fi l.B.!

F I l .C APPENDIX C - KENO.V INPUT

SUMMARY

FI l.C.! +

Fl 1.D APPENDlX D - SAMPLE PROBLEMS - Fl 1.D.1 -

Fi 1.D. I REFERENCES Fi 1.D.14 4

Fi l.vi

,- r--- , - - - , . - , . - c . ,%-,. ---y. . , ,. 3 .,m-w-- g - ..-w . A , , m . wemw e w s- +-g--e ,v .s es--y4

4 Fil.E.1 Fil.E APPENDIX E - KENO-V SAh1PLE PROBLEM OUTPUT Fi l .E.1 Fil.E.1 SELECTED OUTPUT FROM SAMPLE PROBLEMS Fi l.E.59 Fil.E 2 MICROFICllE OF COMPLETE SAMPLE PROBLEM OUTPUT Fil.F APPENDIX F - MICROFICllE CROSS REFERENCE OF VARIABLES USED IN KENO Y Fil F l 1

f Fi l .vii

LIST OF FIGURES Fig. Fi l.2.1. Analytic estimate of the relationship between WTLOW and the variance, of, when WTAVG is 0.5 Fil.2.7 Fig. Fi l.2.2. Analytic estimate ef the relationship between WTAVG and the variance, af, when WTLOW is 1/6 Fil.2.8 Fig. Fi l.3.1. Flow chart of program initiation Fil.3.1 Fig. Fi l.3.2. Flow chart of parameter reading Fil.3.2 Fig. Fi l.3.3. Flow chart of overall program flow F i l .3.4 Fig. E l 1.3.4. Flow chart of input data reading Fl1.3.6 i

Fig Fi l .3.5. Flow chart for reading array data Fil.3.9 -

Fig. Fi l.3.6. Flow chart for reading geometry data F i l.3.10 Fig. F 11.3.7. Flow chart for reading mixing table data Fi l.3.12 Fig. Fi 1.3.8. Flow chart for reading plot data Fi l.3.13 l

Fig. F i l .3.9. Flow chart for reading biasing data Fi l.3.14 Fig. El 1.3.10. Flow chart for reading restart data Fi l.3.15 Fig. Fi l.3.l l. Flow chart for generating remaining data . Fi l.3.16 Fig. Fil.3.12. 1 low chart for mixing cross sections F11.3.18 Fig. Fi l.3.13. Flow chart of mixing operations Fi l.3.20 Fig. Fil.3.14. Flow chart of angle and probability generation Fi l.3.21 _

Fig, Fi l.3.15. Flow chart of mixed cross-section processing Fi l.3.22 Fig. Fil.3.16. Flow chart for writing data on the restart data file . Fi l.3.23 Fig. Fil.3.17. Flow chart for generating correspondence arrays. Fi l.3.24 Fig. Fi l.3.18. Flow chart of super group creation Fil.3.25 Fig. Fi l.3.19. Flow chart for printing macroscopic cross sections Fi l.3.27 Fig. F11.3.20. Flow chart for loadin; supergrouped data Fi l .3.28 Fig. Fl !.3.21. Flow chart for processing geometry . Fi 1.3.29 Fig. Fi 1.3.22. Flow chart for loading data from direct access Fi l.3.31 Fig. Fil.3.23. Flow chart of geometry checking procedure F11.3.33 Filix

L LIST OF FIGURES (cont.) - -

Fig. Fil.3.24. Flow chart for distance to intersection. Fil.3.35 Fig. Fil.3.25. Flow chart for calculating volumes Fil.3.36 Fig. Fil.3.26. Flow chart for loading biasing data . Fil,3.37 Fig. F11.3.27. Flow chart for pictures or plots Fil.3.38 Fig. Fil.3.28. Flow chart of tracking routines. Fil.3.39 Fig. Fil.3.29. Flow chart for loading calculated restart data Fi l.3.42 Fig. F11.3.30. Flow chart for providing initial source distribution - Fi 1.3.4 3 7

Fig. Fil.3.31. Flow chart for tracking individual histories Fi l.3.46 Fig. Ei1.3.32. Logic flow chart for subroutine TRACK F11.3.49 Fig. Fil.3.33. Flow chart for providing the next generation source Fi l.3.54 Fig. F11.3.34. Flow chart for end of generation processing . F11.3.55 Fig. Fi1.3.35. Flew chart for end of problem proccasing . F11.3.56 Fig. Fil.3.36. Flow chart for printing fluxes . Fil.5.37 Fig. Fil.4.1. Examples of geometry not allowed in KENO. Fi l.4.8 Fig. F11.4.2. Examples of correct KENO units. F11.4.9 Fig. Fil.4.3. Example demonstrating HOLE capability in KENO Fi l .4.9 .

Fig. Fil.4 4. Example of array construction Fil.4.10 Fig. El1.4.5. Example of an array composed of nits containing arrays and holes Fil.4.10 Fig. Fil.4.6. . Partially filled hemisphere or hemicylinder less than half full . FIL4.15 Fig. F11.4.7. Partially filled hemisphere or hemicylinder more than half full. . Fi 1.4.15 Fig.Fil.5.1. Stack of disks with a square cap , Fi l.5.10 Fig. Fi1.5.2. Two large cylinders joined axially by a small cylinder . Fi 1.5.16

- Fig. Fil.5.3. Two luge cylinders radially connected by a small cylinder Fi 1.5.17 i Fig. Fil.5.4. KENO V approximations of cylindrical intersections . . Fil.5.17 Fig.Fil.5.5. . Two small cylinders joined axially by a large cylinder Fi l.5.20 Fig. Fil.5.6. Close-packed rods in an annulus. . Fil.5.24 F11.x

r s

LIST OF FIGURES (cont.) -

Fig. Fi l.5.7. Annular rods in triangular pitch lattice. Fi l.5,26 Fig. Fl!.5.8. Configuration using nested holes Fil.5.30 Fig. Fi l.5.9. Complicated geometric arrangement represented by Unit 7 Fil.5.31 -

Fig. Fi l .5.10. Geometric component represented by Unit 4 Fil.5.32 Fig. Fi1.5.1Ia. Left half of printer plot FI 1.5.37 Fig. Fil.5. lib. Right half of printer plot - Fil.5.38 Fig. Fil.5.12. x-y plot of mixed array Fi l.5.42

~

Fig. Fi 1.5.13. x t plot of mixed array Fi l.5.43 Fig. Fi l.5.14. Two racks of uranium buttons Fil.5.45 Fig. Fi l .5.15. Entire storage array in the room Fil.5.47 -

Fig. FI l.5.16. Uranium rods in a cylindrical container Fi l.5.49 Fig. Fl!.5.17. x-y slice of uranium rods in a cylindrical container. Fil.$.52 Fig. Fi 1.5.18. x z slice of uranium rods in a cylindrical container . Fi l.5.53 Fig. Fi l.5.19. Typical FWR shipping cask , Fl i.5.54 Fig. El1.5.20. Simple units . ,

Fil.5.55 Fig. Fil.5.21. Quarter section of fuel pin array Fil,5.56 -

Fig. Fi 1.5.22. Quarter section of fuel assembly Fi l.5.57 Fig. Fi1.5.23. 2 x 6 array of B4C rods.

Fi l.5.58 Fig. Fi1.5.24. Central array .

F11.5.58 Fig. Fl1.5.25. l.ong B4C rod arrays . Fl 1.5.59 Fig. Fil.5.26. Central array with long B4C arrays. Fi l.5.60 Fig. Fi l.5.27. Two fuel assemblies and B4C rods - ,

Fl !.5.60 Fig. Fil.5.28. Associated data for single unit mixture map Fil.5.78 Fig. Fil.5.29. Mixture map of single unit with centered origin - Fi l .5.79 Fig. Fi l.5.30. Associated data for single unit unit map. Fi l.5.79 Fl 1.xi

1.1.VF OF l'IGUltl'S (cont.)

1 ig. Fl1.5.31. Unit map printer plot for single unit with centered origin i 11.5.80 I ig Fi1.5.32. Associated data for mixture map of single unit with offset origin . Fl 1.5.81 Mixture map of single unit wi.h offset origin . F11.5.8 2 I ig. I i1.5.3 3.

i ig. Fi1.534. Associated data for unit map of single unit with offset origin Fi1.5 83 iin Fil.535. x-y plot of 2x2x2 bare array Fi l .5.84 x.z plot of 2x2x2 bare array Fil.5.85 I ig. I 11.$.36 Fi l .5.87 _

Iig Fil.5.37. Plot data for x-y slice of exampic 4 F i l.5.87 l'ig. Fil.5.38. x-y plot of 2x2x2 reflected array F i l.5.88 Fig. I 11.5.39. Plot data for enlarged x-y stiec of example 4 Fi 1.5.88 I ig.1:11.5 40 Enlarged x-y plot of 2x2x2 reflected array Fil.5 89 I ig. Fil.5,41. Plot data for x z slice of example 4 Fig. Fil.5.42. x.z plot for 2x2x2 reflected array .

Fil.5.90 Plot data for enlarged x z r. lice of exampic 4 Fi 1.5.91 Fig.1 11.5.4 3.

Fi l.5.92 Fig. Fil.5,44. Enlarged x z plot of 2x2x2 reflected array F11.5.95 Fig. i;lI.5.45. Plot data for x y shee of example 5 Fil.5.95 Fig. FI1.5.46. x.y plot of 2x2x2 reflected array with centered origin. -

Fil.5.96 Fig. Fil.5.47. Plot data for an enlarged x.y slice of exampic 5 Fi 1.5.96 Fig. F11.5.48. Enlarged x-y plot of 2x2x2 reflected array with centered origin Fi 1.5.97 Fig. Fil.5 49. Plot data for x z slice of exampic 5 Fi l.5.98 Fig. ElI.5.50. x z plot of reflected 2x2x2 array with centered origin.

Plot data for enlarged x-z slice of exampic 5 62 11.5.99 Fig. El 1.5.51.

Enlarged x z plot of reflected 2x2x2 array with centered origin F l 1.5.100 Fig. Fi 1.5.52.

Fil.5.104 Fig. Fil.5.53. Mixture map of nested holes problem Plot data for unit map of nested holes . Fi l.5.104 Fig. F11.5.54 Fil.5.105 Fig. Fil.5.55. Unit map of nested holes problem Fi 1.xii

1 1.lST OF FIGURFS (cont.) .

j Fig. Fil.5.56. Flot dat'a for x-z slice of storage array < Fil.5.106 Fig. Fi1.5.57. x z plot of storage array , , , . . Fil.5.107 Fig. Fi1.5.58. Plot data for x y slice of storage array Fi1.5.108 :

Fig. Fi1.5.59. x y plot of storage array F11.5.108 Fig. Fi l.6.1. Sample KENO Y header page Fi l .6._1 Fig. F11.6.2 Sample program verification table Fl 1.6.2 Fig. F i l .6.3. Sample table of numeric parameter data Fi l.6.2 Fig. Fi l.6.4. Sample table of logical parameter data Fi l .6.3 -

Fig. Fil.6.5. Example of unprocessed geometry input data Fi l.6.3 Fig. Fl i.6.6. Sample table of data sets used in the problem Fi l.6.5 Fig. F i l .6.7. Example of mixing table data . , Fl1.6.6 Fig. Fl 1.6.8. Cumulative probabilitics for correlating the albedo energy group to the cross section energy group Fil.6.6 Fig. Fi l.6.9. Cumulative probabilities for correlating the cross-section energy group to the albedo energy group Fil.6.7 Fig. Fi l.6.10. Example of macroscopic ID cross sections . . Fi l.6.7 Fig. Fi l ,6. l l . Example of 2-D macroscopic cross sections Fi l.6.8 -

Fig. Fi 1.6.12. Example of macroscopic probabilities . Fi l .6.9.

Fig. Fi l.6.13. Example of macroscopic angles . Fi l.6.9 Fig. F11.6.14. Sample table of additionalinformation . Fi 1.6.10 Fig. Fil.6.15. Sample table of space and supergroup information . Fi l.6.12 -

Fig. Fl1.6.16. Example of array summary . - Fi1.6.12 Fig. Fil.6.17. Example of geometry region data; ._. Fil.6.13 -

Fig. Fil.6.18. Example of unit orientation description. Fi l .6. I'4 -

Fig. Fil.6.19. _ Sample volume information . . Fi l.6.15

- FI 1.6.16 -'

Fig. Fi 1.6.20. Biasing information .

Fig. Fil.6.21. Example of biasing data - Fil.6.16 Fil xiii

1,lST OF FIGURES (cont.)

Fig. Fil.6.22. Summary of picture symtals and coordinates. Fi l.6.17 Fig. Fil.6.23. Sample plot representation Fil.6.17 -

Fig. Fi1.6.24. Pre-tracking edits Fi 1.6.18 Fig. Fil.6.25. Example of initial source points Fi l.6.19 Fig. Fi l.6.26. Example of k effectives by generation . Fi l.6.21 Fig. Fil.6.27. Example of the final k effective edit Fi l.6.22 _

Fig. Fil.6.28. Sampk plot of average L-effective by generation run F!l3.23 Fig. Fil.6.29. Sample plot ;l aveiage k-effective by generation skipped. Fi l.6.24 Fig. Fil.6.30. Sample of the final edit of fissions, absorptions, and leakage with region-dependent information suppressed . Fil.6.25 Fig. Fi l.6.31. Samp:,: of the final edit of fissions, cbsorptions, and leakage by region. Fil.6.26 Fig. Fil.6.32. Example of matrix k-effective by unit location. Fi l.6.26 Fig. Fil.6.33. Sample fission production matrix by position index. Fi l.6.27 Fig. Fil.6.34. Example of source vector by position index Fi l ._6.27 Fig. I'l I.6.35. Example oMi.ctor k effective by position index Fil.6.28 Fig. Fil.6.36. Example of matrix k cffective by unit number . Fi l.6.28 .

Fig. Fil.6.37. An example of the fission probability matrix by unit Fil.6.29 Fig. Fil.6.38. Example of the source vector by unit. Fil.6.29 Fig Fil.6.39. Example of cofactor k effective by unit number Fil.6.30 Fig. El1.6.40. Example of matrix k-effective by hole number. F11.6.30 Fig. F i 1.6.41.- Example of fission production matrix by hole Fil.6.30 Fig. Fil.6S.2. Example of source vector by hole number. Fi l.6.31 Fig. Fil.6.43. Example of cofactor k-effective by hole number Fil.6.33 -

Fig. Fl1.6.44. - Example of matrix k-effective by array number Fi l.6.31 -

3' Fig. Fil.6.45. An example of the fission production matrix by array number Fil.6.32 Fi l.xiv

l l

LIST OF FIGURES (cont.)

Fig. Fil.6.46. Example of source vector by array number. Fi l.6.32 Fig. F11.6.47. Etr uple of cofactor k-effective by array number Fi l.6.32 Fig. Fil.6.48. Example of the fission density edit Fi l.6.33 Fig. Fi l.6.49. An example of a flux edit Fi l.6.33 Fig. Fi l.6.50. Example of the frequency distributions Fil.6.34 Fig. El l.D, . Cntical 2C8 bare assembly F i l.D.20 Fig. F i l .D.2.

~

Italf of the paraffin reDected 2C8 assembly before the top reDector was added F1 a.D.21 Fig. Fi l .D.3. Critical assembly of 4 solution units and 4 metal units Fil.D.22 Fig. Fi 1.D.4. Drawing of two cuboids in an annulus critical assembly Fi 1.D.23 Fig. F11.D.5. Drawing of the cylinder in an annulus critical assembly F i l .D.23 Fig. Fi l.D.6. Drawing of a critical assembly consisting of a uranium sphere on a plexiglas collar with a cylindrical water reflector Fil.D.24 Fig. Fi 1.D.7. Perspective of critical iF27 experiment Fi1.D.25 Fig. Fi 1.D.8. View of a 27-unit cubic array with 2.54-cm-thick plexiglas reflector on five sides and a 15.24-cm-thick paraffin base Fil.D.26 Fig. F11.D.9. Typical arrangement for critical experiments with interacting arrays of aluminum cylinders containing enriched 2nU solutions Fil.D.27 -

Fig. F11.D.10. Schematic of bare partially filled sphere experiment inside a 9.5-ft-diameter,9-ft-high steel tank Fi l.D.28 Fi l .xv

LIST OF TAllLES l

l Table Fil.4.1. Types of input data Fil.4J Table Fil.4.2. FIDO like input for mixed box orientation fill option Fi l.4.23 Table Fl1.4.3. Face codes for entering boundary (albedo) conditions . F11.4.27 Table Fil.4.4. Albedo names available on the KENO V albedo library for use with the face codes . Fi l.4.28 Table Fil.4.5. ID's, group structure and incremental thicknesses for weighting data available on the weighting library F11.4.30 Table Fi1.4.6 Starting distributions available in KENO V . Fi 1.4.33 Table Fil.4.7. Summary of parameter data Fi l .4.43 Table Fil.4.8. Summary of array data Fil 4.44 Table F11.4.9. Summary of biasing data F11.4.45 Table Fil.4.10. Summary of boundary condition data Fi l .4.46 Table Fil.4.ll. Summary of geometry data Fi l.4.47 Table Fil.4.12 Summary of mixing table data Fil.4.49 Table Fil.4.13. Summary of plot data Fi l.4.50 Table Fil.4.14. Summary of starting data Fi l.4.51 Tuble Fil.5.1. KENO V 1.ogical Unit Numbers Fi l .5.2 Table Fil.5.2. Structure of RESTART file. Fi l.5.l l i Table F11.5.3. Key of RESTART file variables Fi 1.5.1 > 5 I Table Fil.C.I. Summary of parameter data F i l.C.2 Table Fil.C.2. Summary of array data Fil.C 3 Table Fi1.C.3. Summary of biasing data - Fi l .C.4 Table Fil.C.4. Summary of boundary condition data Fi l .C.5 Table Fil.C.S. Summary of geometry data . Fi l.C.6 Table F11.C.6. Summary of mixing table data F11.C.8 Table Fil.C.7. Summary on plot data Fi l .C.9 Table Fil.C.8. Summary of starting data Fi l.C.10 Table Fi1.D.I. KENO 16-group ilans ..-Roach cross-section library . F11.D.15 Fi l. xvii i

ACKNOWLEDCMEN'IS Many individuals have coctributed signiPeantly to tbc development of KENO V. Special recogni-tion is given to G. E. Whitesides, head of Technical Applications, who was responsible for the concept

and development of the original KENO code. lie has contributed significantly to some of the tect.-

niques utilized in KENO V. S. K. Fraley, formerly of the Nuclear Engineering Applications Depart-ment, is acknowledged for his assistance in implementing the mechanics of supergrouping.

J. T. Thomas has contributed many ideas that have been implemented in the code.

R. M. Westfall has provided consultation, encouragement and benchmarks for validating the code.

The special abilities of J. R. Knight contributed substantially to debugging the code. Appreciation is expressed to C. V. Parks and J. C. Turner for their assistance in reviewing this document.

Special appreciation is expressed to J. C. White of Y 12 and W. R. Golliher of K 25 for provid-ing funding for the development of the

• array of arrays

• and " holes

• options which have significantly enhanced the geometric capabilities of the code.

The contributions of R. J. Patton and L. Norris in preparing this document are gratefully acknowledged.

F11.xix

- . . _ - - . . .. - ._.~.- - _ - . . . . _ - _ . _ - _ - - - _- --- . - . . ~ . - .

ABSTRACT KENO V.a is an extension of the KENO-V Monte Carlo criticality program and was developed for - -

- use in the SCALE system'. In addition to the features available in KENO V, KENO V.a offers versa-tile new Feometry capabilities and in line printer plots of the ' geometry. -The new geometry features include (1) the array of arrays option, (2) the holes option, and (3) variable chords for hemicyhnders -l and hemispheres. -l The array of arrays options allows arrays to be built of other arrays and nested to any depth, subject _ ,

to the availability of sufficient computer memory. The holes option allows the placement of one or -l more geometry regions within other geometry regions. The depth of hole nesting is limited only by the i 2

availability of sufficient computer memory. The variable chords option allows a hemisphere or hemi-cylinder to be as small as non existent or as large as a full sphere or cylinder, or any size in between.

The primary purpose of KENO V.a is to determine k-effective. Other calculate ' quantities include lifetime and generation time, enerFy-dependent leakages, energy- and region-dependent absorptions, fis-sions, fluxes, and fission densities.

KENO V.a retains the KENO V features such as ficxible data input, the ability to specify origins for cylindrical and spherical geometry regions, the capability of supergrouping energy-dependent data, a P, scattering model in the cross sections, a procedure for matching lethargy boundaries between alber*os and cross sections to extend the usefulness of the albedo feature, and improved restart capabinties.

This advanced user-oriented program features simplified data input and efficient use 'oi mmputer  ;

^

storage. This allows the user to readily solve large probler.s whose computer storage requirements and geometric cornplexity precluded solution when using older versions of KENO.

l a

4 Y

Fil.xxi

, _ - , _ , , . - . - - - 4., ~ .- ._;-- - _ - - - __ _ ___________ _ _ _

Fil.1 INTRODUCTION TO KENO V a l This report uses the terms KENO V.a and KENO Y to refer to the KENO V.a program. KENO V.a. a functional module in the SCALE system, is a multigroup Monte Carlo criticality program used to calculate the k effective of a three dimensional system. Special features include simplified data input, supergroup.ng of energy-dependent data, the abdity to specify origins for spherical and cylindri-cal geometry regions, a P scattering treatment, extended use of differential albedo reflection, and an improved restart capability.

The KENO V data input features flexibility in the order of input. 'I'he single restriction is that the title must be entered first and the parameter data, if any, must immediately follow. A large pertion of the data has been awigned default values that have been found to be adequate for many problems.

This enables the user to run a problem with a minimum of input d' ta.

Blocks of input data are entered in the form:

READ XXXX input data END XXXX where XXXX is the key vard for the type of data being entered. The types of data entered include parameters, geometry region data, array definition data, biasing or weighting data, albedo boundary conditions, starting distribution informaiion, the cross-section mixing table, extra 1 D (reaction rate) cross-section ID's for special applications, and printer plot information.

A block of data can be omitt d unless it is needed or desired for the problem. Within the blocks of ,

data, most of the input is activated by using keywords to override the default values.

The geometry input is very similar to that of KENO IV, except the specification of the bias - data -

has been rearranFed to minimize storage requirements. An important improvement is the ability to specify the origin for cylinders, hemicylinders, spheres, and hemispheres. This allows the use of noncon-centric cylindrical and spherical shapes and provides a great deal of freedom in positioning them.

Another improvement allows for hemicylinders and hen,ispheres whose cut surface can be placed at any distance between the radius and the origin.

An additional geometry convenience is the availability of an alternative method for specifying the array definition (mixed box or unit orientation) data. This method utilizes FIDO like options for filling the array.

The most outstanding KENO geometry advancement is the addition of the " array of arrays" and

" holes

• capabilities. The array of arrays option allows the construction of arrays from other arrays.

The depth of nesting is limited only by computer space restrictions. This option greatly simplifies the setup for arrays involving different units at different spacings. The hole option allows placing a unit or an array at any desired location within a geometry region. The emplaced unit or array cannot intersect any geometry region and must be wholly contained within a region. As many holes as will snugly fit without intersecting can be placed in a region. This option is especially useful for describing shipping casks and reflectors that have gaps or other geometrical features. Any number of holes can be described in e Wiem and holes can be nested to any depth.

An important feature of KENO V is the capability of supergrouping the energy-dependent informa.

tion such as cross sections and fluxes. This automatic feature is activated when the computer storage is insufficient to hold the entire problem at once. The energy-dependent data are then broken into super-groups that are written on a direct access device and moved in and out of memory as necessary, Thus larger problems can be run on smaller computers.

Anisotropic scattering is treated by using discrete scattering angles. The angles and associated pro-babilities are generated in a manner that preserves the moments of the angular scattering distribution for the selected group to-group transfer. These moments can be derived from the coefficients of a P, Legendre polynomial expansion. All moments through the 2n 1 moment are preserved for n discrete scattering angles. A one-to-one correspondence exists _ such that n Legendre coefficients yield n moments. The cases of zero and one scattering angle are treated in a special manner. KENO V can recognize that the distribution is isotropic even if the user specifies multiple scattering angles, and -

therefore selects from a continuous isotropic distribution. If the user spuifies one scattering angle, the Fi l . l .1

. ~

-l F11.1.2

- code performs semi continuous scattering by picking scattering angle cosines uniformly over some range  ;

between 1 and + 1. The pebability is rero over the rest of the range.

Differential albedos are available to simulate tracking in a reflector. These albedos were generated using the llan;en-Roach 16 energy group structure. KENO V can extend the use of these albedos to include other energy group structures. This is done by matching lethargy boundaries bet ='een the albedos and cross sections so the appropriate energy transfers can be made. l.ethargy boundary tables are created for both the albedo and cross section energy group structures, and the lethargy interval corresponding to the desired transfer is determined based on a uniform distribution over the lethargy interval. Approximations must be made when the energy group boundaries of the albedos and cross -

sections are different. Therefore the user should scrutinite the results to evaluate the effects of the 3 approximations until an adequate information base is established.

The KENO V restart option is easy to activate. Certain changes can be made when a problem is.

restarted, including the use of a different random sequence and turning off certain print options such as fluxes or the fissions and absorptions by region.

l i-l l

i i

(

Fil.2 TIIEORY AND TECilNIQUES F11.2.1. Tile TRANSI' ORT EQU ATION The equation KENO V solves may be derived in the following manner, starting with the lloltzmann neutron tiansport ;quation which may be written as' I h(X,E,0,i) + 0 V4-(X,E,0,s ) + I,(X,E ,0,t )4'(X,E ,0,1 ) = S(X,E ,0,t )

v dl

( Fi l.2.1 )

+ f {, E,(X,E'-E ,O'-0,t )4-(X,E',0',t )dO'dE' ,

w here:

4-( X ,E ,0,1 ) - neutron flux (neutrons /cm 2/sec) per unit energy at energy E per steradian about direction 0 at position X at time moving at a speed v corresponding to E.

1,( X ,E ,0 t ) = macroscopic total cross section of the media (cm l) at position X, energy E, direction 0 and time i, I,( X ,E '- E ,0'-0,t ) - macroscropic differential cross section of the media (cm'l) per unit energy at energy E' per steradian about direction O' at posi-tion X, and time 1, for scattering to energy E and direction 0, S(X,E,0,t) - neutrons /cm 3/sec bora at position X and time t per unit energy at energy E per steradian about direction O (excludes scatter source).

Defining q(X,E,0,r) as the total source resulting from the external source, scattering, fission and all other contributions, the following relationship can be written.

g(X,E,0,t) = S(X,E,0,t )

(Fi l.2.2)

+f,,{7 I,(X,E '-E ,0'~ 0,t )4+(X,E *,0',t )d n'dE '

Combining Eqs. (Fil,2.1) and (Fil.2.2), assuming the media to be isotropic, ignoring the time depend-ence of the cross sections and converting the equation to multigroup form yields I (Fi1.23)

' (X,0.t ) + 0-V4',(X,0,r ) + I, (X)4+,(X,0,t ) - q,(X,0,t ) ,

r, at '

where:

F11.2.1

Fi1.2.2 g is the energy group of interest, v, is the average velocity of the neutrons in group g, 4',(X,0,t ). is the angular Dus of neutrons having their energies in group g, at position X and time t.

I,,(X) is the macroscopic total cross section of the media at position X for group g, correspond.

ing to f^9 I,(X,E 14-(X,E,0,t )dE E,,(X ) +  ! ,

f 4-(X,E,0.t)dE where AEg defines group g, and q,(X,0,i) is the total source contributing to energy group g at position X, and time t in direction D, Utilizing the relationship X'=X RO, defining the problem to be time-independent, using an integrating factor on both sides of Eq. (F11.2.3), and defining a

T(R) - f 5,(X-R'u)dR* ,

the following equation can be written.

4>,(X,0) - { q,(X RD,0)rH") dR - (Fi l.2.4) -

At this point, the problem becomes an eigenvalue problem. If there is no external source, the source may be defined as q,(X,0) (F11.2.5)

}afdQ't,.(X,D')E,(X,g'~g,Dsa) + f G,(X,0) .

where: -

k is the largest eigenvalue of the integral equation, Q,'( X ,0) is the fission nource at position X for energy group g and direction 0 (all fission con .

tributions to group g from all energy groups in the previous generation), .

I,(X ,g'~g,0' 0) is the scattering cross section for scattering at position X from group g' and direction--

D' to group g and direction D.

In terms of energy, the scatter can be defined as

_ . _ . _ _ _ _ . - ~ _ - - - .

~ .. -.. - = . . -- . . - . ~ =- .- -._~ -- .- . = _ ...-

~ . . ~ - .. ..-

4 Fl 1,2.3 I,(X,g'*g,0_' 0) = . [,?-(,!,3,(X,E'~E 06 0)4-(X,E',0')dE'dE

- (Fi l.2.6) -

Jg,,+(X,E',0')dE'

- where:

AE,is the energy range defining er.ergy group g and AE,. is the energy range defining energy group g'.

Assuming the fission neutrons to be isotropic, the fission source Q,'(X,0) can be written as i G,'(X,0) - f, dO'4,4X,0')x(X,g' g)t.,.(X)!j,.(X) , (F11.2.7) where:

x(X ,g '~g ) is the fraction of neutrons born in energy group g from fission in energy group g'in the media at position X, >

t','( X ) is the number of neutrons resulting from a fission in group g' at position X, I f,4X ) is the macroscopic fission cross section of the material at position X for a neutron in energy group g'.

Substituting Eq. (Fil.2.5) into Eq. (Fil.2.4) yields the following equation:

~

+,(X,0) = { dRe'M*1 1.Q,(X RO,0) i- . .

(Fi 1,2.8)

+ 1 [dO'4',.(X-RO,0')I,(X R0 g'~g,0' 0) .

c'  ;

L The definition of k may be given'as the ratio of the number of neutrons in the (n+ 1)th generation

' to the number of neutrons in the nth generation or the largest eigenvalue'of the integral-equation. -

Using Eq. (Fil.2.7), Eq. (Fil.2.8) can be written as l

w

( +,(x,0> - 5 dRe n 3ps,,a.RO>I,,a.R0)sx.RO,. ,),,a.Ran.)d0; j

~,, ( A .R 0) g &ewd -

ir - - - ' + w -- iin-* *e-e- -n>-7--eem-, y. + -a -n= e-- e 4 --- ---wa e t- w k

Fi l .2.4 Writing Eq. (Fil.2.9) in .* generation notation / multiplying and dividing certain' terms by I,,(X)'and multiplying both sides of the equation by v,(X)I,(X),' f yield the following equation, which is solved by K EN O. --

=

e,(X)!f,(X)

'#(X}+#'*(X'0} ~ e,(X)I ,(X) I(X) dRt'"

• f X) I g(X) 1 e f d O' Th a ,.(X-RO)I z,,4 X-R g) ,'(X-RO)

X 'E # #\* U#' Aw (F11.2.10)

+ [g I,(X R D,g'~g,0' 0) 5,.(X R O)t,. ,(X-R O,0')dn' 3,,,z y,p g; 1 .

where n indicates the nth generation and n-1 is the (n-1)th generation. Note that the left-hand side of the equation, e,(X) If,(X)t,,,(X,0), is the fission production for the nth generation.

The solution strategy utilized by KENO V solves Eq. (Fil.2.10) by using an iterative procedure.

The fission production at point X in energy group g due to neutrons in the (n-1)th generation, normal.

ized to the system multiplication, is I v,4X)If ,(X) 7 [, 3 (y) x(X,g'~g)I,,4X)+, .i(X,0') dQ' 4r The collision points used in KENO are chosen by selecting path lengths from the distribution g T(R )

which is the probability of transport from any position X-RO to position X.

The first collision density of neutrons in group g Per unit solid angle about 0 resulting from the fis-sion source produced by the (n 1) generation, normalized to the system multiplication, is

=

3 v,.(X RD)I f,4X RO)

I's,(X){ dRe'D*) 3], Z,,4,,p g } .

x(X-R O,g'~g )I, ,(X-R O)4,. ..i(X-R O,0') dQ'

- - . - . - . . . . . - _ . = . . . . _ . . . . . .

Fi l .2.5 The scattering source at position X emerging in group g and direction O resulting from previous colli-sions in the same generation,is I,( X,g "g ,O'- 0)

1. [. y

~ . w cosg + cosysint 4 - " sing sinn ,

dv 2+ w2 Jr 42 w2

Fil.2.6 where:

sin ( - VI-u3 ,

cosi -g - cosine of the scattering angle, n- a random azimuthal angle between 0 and 2r.

Fl1.2.3 111ASING OR WElGIITING In order to minimize the statistical deviation of k effective per unit computer time, KENO V utilizes _

weighted tracking rather than analog tracking. Weighted tracking accounts for absorption by reducing the neutron weight, rather than allowing the neutron history to be terminated by absorption. To pre-vent expending excessive computer time tracking low weight neutrons, Russian roulette is played when the weight of the neutron drops below a preset weight, WTLOW. Neutrons which survive Russian rou-lette are assigned a weight, WTAVG. The value of WTLOW and WTAVG can be assigned as a fune-tion of position and energy. The values used by KENO V are:

DWTAV - 0.5 is the default value cf WTAVG, WTAVG-D%TAV is the weight given a neutron that survives Russian roulette, and WTLOW = WTAVG/3.0 .is the value of weight at which Russian tuulette is played.

A study

• by Hoffman shows these default values to be reasonable for bare critical assemblies.

Figure Fil.2.1, from this study, shows the analytic relationship between the variance and WTLOW when WTAVG is 0.5. Note that the default value of 0.167 for WTLOW is very close to the minimum point on the curve. Experimental results of actual Monte Carlo calculations . Sprovide further assurance -

that 0.167 is an optimum choice for WTLOW when WTAVG is 0.5.

Figure Fil.2.2, also from the Hoffman study, shows the analytic relationship between the variance and the value chosen for WTAVG for a value of WTLOW-0.167. Although the KENO default value for WTAVG is not the optimum, a close examination of the data shows the variance to be changing rel.

atively slow'as a function of WTAVG. While this study shows a value near 0.26 to be optimum for-.

this system, further studies of other systems are needed before changing the default value of WTAVG' froin the 0.5 that has been used in previous versions of KENO.

Inside a fissile core, the importance of a neutron is a slowly varying function in terms of energy and position. llence, for many systems, the standard defaults for WTLOW and WTAVG are good values to use. For reflectors, however, the worth of a neutron varies both as a function of distance from the fissile material and as a function of energy. As a neutron in the reflector becomes less important rela-tive to a neutron in the fissile region, it becomes desirable to spend less time tracking it. Therefore a space and energy-dependent weighting or biasing function is used in KENO V to allow the user to minimize the variance in k-effective per unit tracking time. When a biasing function is used in a reflec-tor, it becomes possible for a neutron to move from one importance region into another whose WTLOW -

is greater than the weight of the neutron. When this occurs, Russian roulette is played to reduce the number of neutrons tracked. -When the reverse occurs, that is, the neutron moves to a region of higher -

importance, its weight may be much higher than WTAVG for that region. When the weight of the neutron is greater than a preset value, WTHI, the neutron is split into two neutrons, each having a

Fi 1.2.7 weight equal to one-half the weight of the original neutron, This procedure is repeated unti! the weight of the split neutron is less than WTill. The default value for WTill is WTAVG'3.0. WTill is the weight at which splitting occurs.

The weiFhting or biasing function for a given core material and reDector material can be obtained by using the adjoint solution from S, type programs for a similar (usually simplified) problem. This adjoint flus gises the relative contributio, of a neutron at a given energy and position to the total fis-sions in the system. The weighting fenction for KENO is thus proportional to the reciprocal of the adjoint flux. Although such a function can be difficult to obtain, the savings gained makes the effort worthwhile for many of the materials that are frequently used as reflectors. Biasing functions have been prepared for several reflector materials commonly used ir KENO calculations. The use of biasing to minimize the sariance in k-effective per unit computer time will usur.lly increase the variance in other parameters such as leakage or absorption in the reflector.

.e:. . - : ,

c :::* - /-

t

/

/ .

/

/

c x:a - -

e4;v T.C x s ,

! l ei  ! \

i ec:n

! t i

co _ . / -

j M ENo CUAutt l

1 i i

I t' o::r o 0 :' oC O 'M O2O C OS a!; 33S JC ATLOW Fig El1.2.1. Analytic estimate of the relationship between %TLOW and the variance, of, when %TAVG is 0.5.

i

-'j

F11.2.8  ;

o 0033 , , , ,

w T Low a Y6 R E I40 DEFAULT w o0032 -

"ii o.0031 -

,WTLOW I I I I I o0030 o to o 25 0 35 c.45 o ts WTAVG Fig. Fil.2.2. Analytic estimate of the relationship between WTAVG and the variance, a,2, when WTLOW is 1/6, 4

p._

'., ~

~b

'- - '-- a ., , , , ,,. , ,,_,, , - . . ,

l Fi l.2.9 fil.2A DIFFERENflAL ALilEDOS j Arrays reDected by thick layers of material having a small absorption to scatterms ratio may require large amounts of computer time to determine k effective because of the relatively long time a history may spend in the reDector. A differential albedo technique was developed for use with the KENO codes to climinate tracking in the reflector. This involves returning a history at the point it impir x on the renector and selecting an emergent energy and polar angle from a joint density func.

tion , endent upon the incident energy and polar angle. The weight of the history is adjusted by the functional return from the reflector, which is also based on the incident energy and angle.

The characteristics of a differential albedo emulate the attributes of the reflector material and are independent of the material or materials adjacent to the reDector. Thus, a differential albedo that is generated for a given renector material can be used with any array, regardless of the type of fuel or fis-ule material contained within the array.

For riany calculations involving reflected arrays of fissile material, the differential albedo treatment is a mmerful tool that can significantly reduce the computing time required to determine L effective.

The savings will vary, depending on the importance of the reflector to the system. A substantial effort is required to generate a differential albedo, but the savings gained are well worth the effort for com-monly used renector materials.

To generate the differential albedo information for a material, a Oxed source calculation must be made for each incident energy and angle. The data presently available for use with KENO were gen.

erated by one-dimensional discrete ordinates caknations for slab geometry, representing infinits, slabs.

Consequently, for a finite reDector, these data w . not correctly treat histories that enter the reDector near an edge. Past experience with differential albedo redectors indicates that k effective appears to be conservative for small faces and will tend toward the correct result as the face becomes large relative to the area near the corners. Therefore care must be taken to ensure that any surface to which a differen-tial albedo is applied is large enough that the errors at the edges can be ignored.

Because differential albedos are expensive and time-consuming to generate, those corresponding to the llansen-Roach 16 energy group structure are the only differential albedos currently available for use with KENO. In the past, their use was limited to problems utilizing cross sections having the llansen Roach 16 energy group structure. KENO V extends the use of differential albedos to other energy group structures by allowing appropriate energy transfers. TP is accomplished by creating lethargy boundary tables for the albedo group structure and the cross se~on group structure and deter.

mining the lethargy interval corresponding to the desired transfer (cross section group structure to albedo group structure or vice versa) based on a uniform lethargy distribution over the irmtval. When the energy group boundaries of the cross sections and albedos are different, the rescits should be scru-tinized by the user to evaluate the effects of the awoximations.

Fil 2.5 SUPERGHOUPING An important feature of KENO V is the capability of supergrouping energy-dependent information.

This includes the cross sections, albedos, pointer arrays, weights, leakages, absorptions, fissions and Guxes. If the available cwouter memory is too small to Ltd all the problem data at once, KENO V determines the number of supergroups necessary to allow execution of the problem. A. problem cannot be supergrouped if the cegy dependent d.sta associated with any individual energy grot p are too large to fit in the Tilable narnory, if enough memory is available to accommodate s.ll the energy.

dependent dats r( once, only one supergroup is created. Once the number of supergroups has been determined, the energy-dependent data are arranged in supergroups and are written on the direct access supergroup file. During execution cf a problem, the supergrouped data are moved in and out of mem-ory as necessary.

. __.____m._ .. _ _. _ . _._ _ _ = _ _ . _ _ _ _ _ _

- F I 1.2.10 The advantage of supergrouping is that larger problems can be run on smaller computers. This capabiht) is gained at the espense of running time and increased I/O's. The more supergroups, the more I/O's are usul and the slower the problem will run because of the banking, sorting, and use of direct access d wices in the solution of the problem.

In order to reduce the amount of data movement between memory and the direct access 6upergroup file, KENO V rnaintains a bank of histories (the neutron bank) and follows all those histories that fall within the current supergroup before going to the next supergroup. Histories that are scattered out of the current supergroup are placed back in the bank. When all the histories in the current supergroup have been processed, the bank is sorted, placing the histories for the most populous sepergroup at the top of the bank. All other histories are placed at the bottom of the bank. The data for the most popu.

lous supergroup is then brought into memory and tracking proceeds.

I i1.2.6 RESTART KENO V incorporates a versatile and convenient restart capability. The decision to write a restart file requires the user to specify only the number of generations between writing restart data and the unit number where the restart file is to be written. A file definition card must be included in the job control language for the restart data file. The input data are the first data written on the restart data file. The group-dependent input data are written a group at a time. This includes the cross sections, albedos, pointer arrays and weights. The number of records of input data is automatically determined by the code and written on the restart data file. After the input data htve been written on the restart data file, the calculated data are written at the end of each specified generation. These data include the generation number, random number, number of histories per generation, number of energy groups, bank lengths, common information, the k-effectives by generation, the neutron bank, the fission densi.

ties. matris arrays, and the calculated group-dependent data. These group-dependent data are written a group at a time and include leakaFes, absorptions, fissions and fluxes.

The KENO V restart capability allows a problem to be restarted at the first generation with differ-ent input because all data input supersedes Jata from tne restart data file.

If a problem is to be restarted at a generation greater than one, the only data that can be changed are certain parameter data. Changes in the parameter data that are not allowed include (1) requesting fissions and absorptions by region if they were not requested by the parent case, (2) requesting fission densities and fluxes if they were not requested by the parent case (3) requesting matrix information that was not requested in the parent case, and (4) changing the configuration of the neutron bank to be ,

different from that of the parent case.

11ccause restart d;.ta are written a group at a time, a problem may be restarted with an entirely dif.

ferent supergroup structure.

if a problem is to be restarted following a generation for which restart data were not written, the code will write a message and restart with the next available generation for which restart data exist, if no such generation is found, the problem is terminated.

I

1 Fi l.2.l l I'll,2.7 GEOMETRY KENO geometry is restricted to the use of specific shapes. These shapes are called geometry regions or regions. Allowed shapes are cubes, cuboids (rectangular parallelepipeds), spheres, cylinders, heinispheres, and hemicylinders. These shapes must be oriented along orthogonal axes and cannot be ,

rotated. They can be translated. Hemispheres and hemicylinders are not limited to half-spheres and half cylinders, the definitive plane can be positioned by entering a chord. The value of this chord can range from the positive magnitude of the radius (giving a complete sphere or cylinder) to the negative magnitude of the radius (giving a rero volume, nonexistent sphere, or cylinder).

A major restriction app lied to KENO geometry is that intersections are not allowed Furthermore, each successive geometry region must completely enclose the preceding region. Tangency and shares faces are allowed. The volume of a region is the volume of the specified shape minus the volume of the preceding region shape. To alleviate the complete enclosure restriction, KENO allows multiple sets of geometry regions with each set independently governed by this restriction Each set of these multiple geometry regions are called units or box types. Units can be stacked together in a three dimensional rectangular parallelepiped called an array or lattice just as children's blocks can be stacked. Units that are to be stacked together in this manner must have a rectangular parallelepiped outer region and the adjacent faces of adjacent units must be the same size and shape. An array can be treated as a build-ing block and be used as a unit within another array.

The use of holes in KENO V.a allows a unit to be emplaced within another unit, thereby alleviating-the restriction that each region within a unit must completely enclose all preceding regions within that unit. However, a hole is not allowed to intersect other holes or regions. A unit that is to be used as a hole need not have a rectangular parallelepiped as its outer boundary.

Multiple arrays can be described in KENO V.a. The global array in an unreflected problem is the outermost array in the problem geometry description. The global array in a reflected problem is the .

array referenced by surrounding geometry regions following the last array placement description that does not immediately follow a unit number description. See Sect. Fil.4.5.

Consistent with past versions of KENO, KENO V.a retains the capability of running a single unit problem. A single unit problem is anc that has no array description.

Fil.

2.8 REFERENCES

1. Robert V. Meghreblian and David K. Holmes, Reactor Analysis, McGraw-Hill (1960).

l 2. J. E. Powell and C. P. Wells, Differential Equations, Ginn Company (1950).

l 3. E. A. Straker, P. N. Stevens, D. C. Irving, and V. R. Cain, The Morse Code - A Multigroup

. Neutron and Gamma Ray Monte Carlo Transport Code, Appendix B ORNL-4585 (1970).

l 4. T. J. Hoffman, The Optimization of Russian Roulette Parameters for Keno, ORNL/TM 7539 l

(1982).

l S. L M. Petrie and N. F. Cross, KENO IV An improved Monte Carlo Criticality Program.

ORNL-4938 (1975). Also see Sect. F5 of the SCALE manual.

6. J. R. Knight and L M. Petrie, 16 and 123 Group Weighting Functions for KENO, ORNL/TM 4660 (1975).

7. G. E. Whitesides and J. T. Thomas, "The Use of Differential Current Albedos in Monte Carlo Cri-ticality Calculations," Trans. Am. Nucl. Soc.12,889 (November 1969).

FI1.3 LOGICAL l'HOGRAh! FLOW

't he general now of the KENO V program during the solution of a problern is given in this s'ec-tion. A formal now chart is not in:luded because of the voluminous nature of the program. The logi-cul program now is broken up into small sections. The format of each section includes an abbreviated now chart, a brief explanation of the purpose of that section of the program, and a brief description of each subroutine involved. The abbreviated flow charts are drawn with KENO V subroutine names contained in boses and library routines as bare names. An arrow in the flow chart indicates that the subroutine associated with the arrow will be treated in detail later in the section.

I'll.3.1 PROGRAM INITI ATION OHf4L ~ DWG 8019???R?

MAIN I I o

INITAL ALOCAT o m

O lll l l l b68;$y$

ggb c: t >

PARAM MASTE R

t. .n my c3 c

>o>

o 3 o

. m i f if lig. Fil.3.1. Flow chart of program initiation The function of this portion of the program is to initialire information, print a header page, call the parameter reading subroutine PARAM, access subroutine MASTER with the storage space allocated by subroutine ALOCAT, and close out the direct access files when the problem is completed or terminated.

M AIN - This subroutine sets flags to specify the proper mode of data reading for the stand alone KENO V program. INITAL is called to perform some initialization. M ASTER is then called from ALOCAT with the requested storage allocation. The direct access files ate closed out by CLOSDA when a problem is completed or terminated.

INITAL - This subroutine calls library routines to perform initialization and print a header page, it then reads the problem's title card and parameter read Dag and calls subroutine PARAM to do the actual reading of the parameter data.

JSTIM E - This call to the library routine JSTIME is for the purpose of storing the initial time in COMMON /I INAL/ for timing purposes.

LISTQA - 'this library routine provides a program verification page for quality assurance purposes.

Fi l .3.1

Fi l.3.2 IOLLIT - This call to the library routine IOLEIT is for the purpose of storing the initial 1/0 count in COhihtON/ FINAL / for future calculations that indicate the number of 1/O's used ta certain parts of the program.

SCANON This library routine is called to activate the feature that allows scanning for 4he word END when reading data.

h1ESAGE This library routine is called with two arguments, an eight character hollerith argument and an output unit. Additional library routir. s are called frorn htLSAGE to print a header page in block letters. The header paFe includes the eight character hollerith argu-ment ( KENO- Y ), the date, the time execution was begun, and the job name.

AREAD- This library routine is used to read alphanumeric data. It is used here to read the title card and the parameter reading flag.

l'A R A h! - This subroutine is called to set default values for the parameter input data and to read parameter data, See Sect. Fil.3.2 for a more detailed description of PARAh!.

l ALOCAT- This assembly langtage library routine is called with two arguments. The first argument is a subroutine name and the second argument is the maximum number of words of stor.

age to be alk>cated. ALOCAT calls subroutine hiASTER with two arguments, an array name and the length of the array.

h1AS1Elt- This subroutine is called by subroutine ALOCAT. It is the controlling subroutine for the bulk of the KENO V program flow. See Sect. Fil.3.3 for a more detailed description .

of subroutine hiASTER. I CLOSDA- This library routine is called to close out each direct access file at the normal completion or normal termination of a problem.

Fil.3.2 l'ARAhiETER DATA ORNL-DWG 8319244H PARAM I

I IIIIIII P$55$EEG:-

m m>mmoO >- m

>D >o O O> O '; Co >

-y n Fig, Fil.3.2. Flow chart of parameter reading

-l l

Fil,U j ilon of this section of the program is to set default va lues for t eh parameters and to read tb . .u ? e ,r input data.

9 PARAM - This subroutine is responsible for reading the parameter input data and setting default values for the parameters. The library routine CLEAR is used to zero parameters that are defaulted to zero. The parameter data block is read using AREAD, IREAD, ,

FREAD and ZREAD. Each entry in the parameter data block uses a keyword so the l code can store the parameter data in the correct location. If the problem is a restart problem, restart information including the title of.the original case, parameter data and some ccenmon inforriation is read from the restart data file. The defaulted and input parameter tables are printed by PARAM. Some preliminary data checking is done and appropriate warning and error messages may be printed.

CLEAR - This library routine is called to zero the parameters that are defaulted to zero.

AREAD - This library routine can be called many times from subroutine PARAM. It is used to read parameter names and alphanumeric parameter data.

IREAD- This library routine can be called many times from subroutine PARAM. It is used to ,

read integer parameter data.

FREAD - This library routine can be called many times from subroutine PARAM. It is used to read floating point data, i

ZREAD - This library routine can be called from subroutine PARAM in read 's hexadecimal ran-dom number that will be used as a kernel for the random number package.

RNDIN - This library routine is called from subroutine PARAM to transfer the random number read by ZREAD to the random number package. It is called only if a random number was entered as parameter data. ,

RNDOUT This library routine is called from subroutiae PARAM to preserve the current random number so it can be writtcn on the restart data set and printed in the parameter data.

TIMFAC - This library routine is called from subroutine PARAM to provide the proper adjustment factor by which the allotted tire is melliplied. This factor adjusts the execution time for execution on different computers.

4

, , --w.. , , . ~,,,e, n ,-n-,.,----, . , ,n- --,-,-,,,--,------~-v,--, - , - - - . , - . , . , , - , - - . , - - - - . , - , -

r F11.3.4 l'11.3.3 O\T.R Al.1, PROGR Ah! I 1.OW

.. ,i.

2 a az u , i mi. r

t. t, r -

i 'aj6- , 1 '

l3 iI ! ? 6(! ) 6 4. l /a e e o e o o o nie. 4, e, t i: .n .

m .

}

i e Fig. Fil.3 3. I' low chart of overall program flow The purpose of this section of the program is to direct the primary flow of KENO V. This covers the complete scope of the program from data reading to editing and printing the results.

hi ASTER - This subroutine controls the primary flow of KENO V. It initialires the direct access fi!cs and calls subroutines to read, check and print the input data, calls the tracking rou-tines and prints the calculated results. The number of 1/O's used during various opera-tions is calculated and printed. The following subroutines are called from htASTER as indicated.

SU11 ROUTINE FUNCTION CONDITION OPENDA initialize direct access always IOSDUN initialire I/O's always DATAIN scad input data always hilXER mix cross sections if mixing table is read ICEhtlX read ICE mixed library if cross sections are not j to be used from the restart data file WRTRST write restart information if a unit is defined for writing restart information CORRE generate albedocross- if differential albedo data section information is used NSUPG cicate supergrouped data always POINT calculate pointers always JohitTY primarily controls geometry processing always PRTPLT prints specified plots if a plot data block is entered and the plot option is not turned off CLEAR initialiies arrays where calculated always data is stored LODWTS load biasing data from always direct access into memor- -

GUIDE control tracting alw ays KEDIT edit calculated results always FITFLX load flutes for printing if fluxes are calculated print frequency distribution always '8' FREAK JSTIN1E timir.g always s 1

P Fi l.3.5 OPENDA- This library routine initializes the direct access files.

IOSDUN- This subroutine is called several times to indicate the number of 1/O's used for various operations.

DATAIN - This subroutine controls the reading of all input data except the title card and param-eters. It is explained in more detail in Sect. Fil.3.4.

MIXER - This subroutine is called only if mixing table information is to be entered as data, it con-

• trols the mixing of cross section information and writes a Monte Carlo formatted mixed cross section library for use later in the program. More details are contained in

• Sect. Fi l.3.5.

ICEMIX - This subroutine reads the Monte Carlo formatted mixed cross section library and manipu-lates the cross sections to obtain the cross-section information used by KENO V. This information is then written on the direct access data file. See Sect. Fil.3.6 for addi-tional information.

WRTRST This subroutine is called if a unit has been defined on which to write restart information.

The functicti ui WRTRST is to write restart information as explained in Sect. Fil.3.7.

CORRE- This subroutine is called only if the albedo data block specifies differential albedo data, it cicates lethargy boundary tables and pencrates albedo cross-section energy group corre-spondence information. See Sect. Fil.3.8 for additional details.

NSUPG - The purpose of this subroutine is to create supercrouped information and write it on the direct access file as described in Sect. Fil.3.9.

POINT - This subroutine calculates pointers to access data in memory.

JOMITY - This subroutine is primarily responsible for generating additional geometry data, checking the geometry data, writing appropriate geometry error messages, and printing the Feome-try that is used in the problem. Section Fil.3.10 contains additional details.

LODWTS This subroutine reads biasing information data frorn the direct access data file, loads it into memory and prints it as described in Sect. Fil.3.II.

PRTPLT - This subroutine is called to generate and print two-dimensional printer plots representing slices through the geometrical representation of .the physical problem. See

Sect. Fil.3.12 for additional details.

CLEAR - This library routine initializes arrays where the calculated data are stored.

1 GUIDE - This subroutine guides the flow of the program through the actual tracking of each his-tory. See Sect. Fil.3.13 for a more detailed explanation.

L

a Fi l.3.6 KEDIT - This subroutine is responsible for editing the k-effectives and printing the various informa-tion calculated by KENO V. Section Fil.3.14 contains additional details. -

FITFLX - This subroutine is called only if fluxes are calculated. Its purpose is to determine the masimum number of regions for which fluxes can be contained in memory and to print the fluxes. A more detailed description is contained in Sect. Fil.3.15.

FREAK- This subroutine is called to generate and print the frequency distribution of the k cffective calculated for each generation. The library routines SQRT and EXP are utilized in these calculations.

JSTIM E - This library routine is called at the completion of a problem to compute the total amount of time used.

Fil.3.4 PR0llLEM DFSCRIPTION

- - . > . . > . ~

De ?. A I

ll l -l 1 I I I I -l

j . ...] H- j ~n. } l mm l p 1.a l j -1 l g E

I l 1 I II II I I I jj j w..-

l1' jE lj 5 j i [ an.u l

{=fij

• i

!-- E i j j ....,q j..,.j j-l [ .csm l p-l po...s l j,u.1 i l lIII t f i i 1115 E E5E Fig. Fil.3.4. Flow chart of input data reading This section of the program controls the reading of the input data, excluding the title card and parameter data. After the data have been read, they are written on the direct access data fiic.

DATAIN - This subroutine controls all the data reading with the exception of the title card and parameter data. It initializes COMMON /STDATA/, the common that contains the start data, and initializes the MT array that contains the ID's of the 1 D cross sections that are to be utilized in the problem. The data reading is accomplished by reading blocks of data as described in the data guide. A keyword precedes the data, indicating the type of data to be read. After reading the keyword, the appropriate subroutine is called to read the accompanying data block. After the~ data block RDBOX has been read, it is written on the direct access data file. IOWRT is called several times to gener-ate a table that lists the unit numbers used by KENO V, their names, data set names and the volume containing the data set. This table can be valuable for quality assurance applications. Subroutine FLDATA is then called to supply information that was not entered as data.

Fi 1.3.7 CLI.AR - This library routine is called to initialire COMMON /STDATA/. If biasing data are entered, it is called to clear the space that wdl contain the biasing data. CLEAR is called with two arguments, a beginning location and a length, it initializes allincluded locations to tero.

AREAD - This library routine is used to read the READ flag, the keyword for the type of data to be read, the END flag and the keyword for the type of data just completed. it 'ean be called many times from DATAIN.

R1 - This subroutine is called to write data on the direct access data file. Il passes information between DATAIN and RITli.

RIT E - This library routine is called from RT to write an array of data on the direct access data file.

ARAYIN - This subroutine is called to read data defining the array site. It also reads the unit orien-tation data if any are entered as data. ARAYIN is not called for a single unit problem.

See Sect. 1:11.3.4.1 for additional information. Data input for the array data block is described in detail h Sect. Fi1.4.5.

RTARA- This subroutine is called only if ARAYIN is called. It reads the array data from the scratch unit and writes them on the direct access device.

EXTR A - This dummy subroutine is provided to allow the user to input extra data that are not nor-mally processed by Kl!NO Y. The user must provide the programming to read and uti-lite the data.

GEOMIN This subroutine is called to read the geometry region data. See Sect. Fil.3.4.2 for addi.

tional information. The geometry region data block is described in . detail in Sect. Fl1.4.4 IDXI D - This subroutine is called if the number of extra 1 D cross sections is greater than zero and an extra 1 D data block is entered. It reads the extra l D ID's and loads them into the MT array. The data reading is accomplished using the library routine IREAD. 'Sec-tion Fil.4.9 describes the data input for defining extra 1 D data.

MIXIT - This subroutine is called to read the mixing table data block that defines the mixtures that are to be created. Section Fil.l.4.3 explains the mixing procedure in more detail.

~

RDREF- This subroutine is called to read the boundary conditions (or albedo options) that are to be applied at the outer boundaries of the system described by the geometry data and the unit orientation data. The boundary condition data block is read using the library routine AREAD. Some preliminary data checks are made to detect invalid face code names and incompatible boundary conditions. Section Fil.4.6 describes the data input for defining .

the boundary conditions.

t .

Fi1.3.8 RDSTRT - This subroutine is called to read the start data block that is used to define the spatial dis-tribution of the initial generation. The library routine AREAD is used to read the key. ,

words associated with the start data. IREAD and FREAD are used to read the integer i

and floating point start data, respectively. The library routine 10 is used to write the start data associated with start type 6 on the scratch data file. Data input for defining the initial source distribution is described in Sect. Fil.4.8.

SAVST6- This subroutine is called to save the data associated with start type 6. SAVST6 is called only if start type 6 was specified in the start type data. Sea Sect. Fil.4.8 for start type information. The library routine CLEAR is called to initialize the arr,iy that will contain the start data arrays. The library routine 10 is used to read the start data array from the scratch data file and load it into memory. The library routine MOVE is used to move the start data array into the neutron bank. The library routine RITE is called to write the neutron bank data on the direct access data file.

RDPLOT- This subroutine is called to read the plot data block that is used to generate printer plots.

Section Fil.3.4.4 explains the processing of the plot data in more detail. Section Fil.4.ll describes the plot input data in detail.

WRTPLT This subroutine reads the plot data block from the scratch data file and loads it on direct access. 10 reads the data from the scratch data file and loads it in memory. RITE writes the data on the direct access data file.

RDBI AS - This subroutine is called to read the biasing or weighting data to be used in the problem.

See S-ct. Fil.3.4.4 for more information. The biasing input data block is described in detail in Sect. Fil.4.7.

IOWRT - This subroutine is called with five arguments. They are,in order,(1) the output unit,(2) a four-character hollerith name representing a unit name,(3) the unit number represented by the second argument, (4) the number of words of hollerith information contained in the fifth argument, and (5) hollerith information to be printed. IOWRT is called several times to generate a table of the unit numbers, their names, the data set names, and the volumes on which each resides.

DTASET - This library routine is called from IOWRT to provide the data set name of the requested I/O unit and the volume on which it resides.

RDRST - After the data reading is complete, this subroutine is called if a unit containing data for restarting the problem has been defined. It loads data from the restart data file as described in Sect. Fil.3.4.5.

FLDATA - This subroutine is called to supply default data for arrays that were not entered as input.

-Section Fil.3.4.6 contains a more detailed account of the exact procedure.

lil l,1.9 t

I'l1.3 4 i Arrar hara Ol1Nie DWG (10-1974 lit 3 AR AYIN I

3.-~ m n <

(3 x I H r m IlOX HDDOX RCliRS

$ y] 52 @ $2 yl --

o U I o

_ 'D b x 0 m liLf WRD x$$

3 m $,o m O 0 2. N Y EU Fig. Fil.3.5. Ilow chart for reading array data This section esplains the procedure involved in sending the array data used in the problem.

ARAYIN . This subroutine is called from DATAIN when the words Rl!AD ARRA are encountered.

It is resjonsible for reading the data parameters that define the slic of each array. The unit orientation array data block for each array is read by lit.FWRD for the I'llt, option and by RDilOX for the 1,00P option, llOX then writes .he array data on the scratch data file, The data reading is done using the library routines AltliAD, liti!AD, and YRl!AD. Section Fil.4.5 describes the data read by this subroutine.

ARl!A D - This library routine is used to read the keywords associated with the array data. ,

IRl!A D - This library routine is used to read the integer data associated with the array data.

STOP - This library routine is called to write an error message and stop if insufficient memory is .

available to accomm(xlate the unit orientation array.

YRl!AD - This library routine is called to acad the unit orientation data for the FILL option.

IlLFWRD This bubroutine is called only if the iILL option is used for entering the unit orientation data. The purpose of IILFWRD is to convert the unit orientation arrav data from full word integers to half word integers.

I IlOX - This subroutine is called to write the array data on the scratch data file.

1 .

-, . _. _ . . -, , - ~ . - -.

Fi l.3.10 RDBOX - This subroutine is called only if the LOOP option is used for entering the unit orientation data. It uses the library routine IREAD to read the unit orientation data. Some data consistency checks are made and appropriate error rnessages are written if errors are encountered. If the input geometry is to be printed, RDBOX prints the unit orientation for each array, s associated with an array. GETPTR is used RCllRS - This subroutine is used to read the commer to return the current pointer in the input buffer. RSTPTR resets the pointer. AREAD is used to read the input data and RCRDLN sets the length of the input buffer. STOP is called to write an error message and stop if the array comment is too long (i.e., the end-ing delimiter is missing).

Vll.3.4.2 Geometry Data ORNL-DWG BO 19239R3 GEOMIN I I n

KENOG m READGM I I m 2 $

9 c >U l I I I I e

XXIN XXINA RDORGN o RCHRS 1 I i i I I ,

I i i!

g m 3

g m n >

m m n 2 > :n o m ommmH m m m m m :D m H H O m.

b o b b b Fig. F11.3.6. Flow chart for reading geometry data This section of the program reads the geometry data.

~ * - - , - . . . - . , , - - . . , , , _ _ - , , . , _ , _ , _ _ ., ,_

i l

1 1

Fi l.3.l l GEOMIN This subroutine controls the reading of the geometry data. KENOG is called to read each geometry region specification and write it on the scratch dats unit. Pointers for the data arrays are then calculated and CLEAR is called to initialire the data arrays. . l READGM is called to read the data from the scratch data unit and load them into the 1 appropriate data arrays. The data block read in this portion of the program is described in Sect. Fil.4.4.

KENOG- This subroutine uses AREAD to read the geometry word. IREAD is called to read the unit number for a unit or box type, it is also used to read the number of reflector regions on a reflector card. XXIN is called to read the mixture number, the bias ID number and the geometry dimensions. The origin specification, if any, associated with a sphere, hemi.

sphere, cylinder or hemieylinder is read by RDORON. The chord specification, if any, associated with a hemisphere er hemieylinder is also read by RDORGN. The necessary geometry data bksck is written on the scratch data unit. If the input geometry data block is to be printed, KENOG does this as the data are read.

XXIN - This Subroutine is called to read the mixture number, the bias ID number and the geome-try dimensions. ! READ is used to read the mixture number and bias ID number.

FREAD is used to read the geometry region dimensions.

XXINA - XXINA is an entry point in XXIN. It is called when the geometry word ARRA or ARRAY is encountered. It reads the mixture number and the geometry dimensions.

IREAD is used to read the mixture r umber. FREAD is used to read the geometry region dimensions.

RDORON This subroutine uses AREAD to read a word. If the word is ORIGIN,it uses FREAD to read the points defining the origin. If the word is Cl!ORD, it uses FREAD to ' cad the offset of the plane with respect to the origin. If the word is not ORIGIN or CilORD, a flag is set to prevent KENOG from attempting to read another geometry word.

RCllRS - This subroutine is used to read 'he comment associated with a unit in the geometry region data. GETPTR is used to return the current pointer in the input buffer. RSTPTR resets the pointer. AREAD is used to read the input data and RCRDLN sets the length of the input buffer. STOP is called to write a message and terminate the problem if the com.

ment is too long.

READGM - This subroutine reads the geometry data from the scratch data unit and loads them into the proper arrays.

Fi l.3.12 VI1.3.4.3 Mining Table Data ORNL-DWG B019230 MIXIT P

l II I I I s;5I$ 2H mm m mO

> > O >O >m m oo flDMIXT Fig. Fil.3.7. Flow chart for reading mixing table data This section deals with reading the mixing table data.

MIXIT - This subroutine uscs AREAD to read the mixier keywords and the scattering keyword.

IREAD is used to read the mixture numbers and the numtm. of scattering angles as well as the nuclide ID's. FREAD reads the number densities. The necessary data arrays are written on the scratch data file. Peinters are calculated for the necessary storage arrays and RDMIXT is called to load the data from the scratch file into the storage arrays.

STOP- This library routine is called from MIXIT if the storage space is insufficient to hold the mixing table arrays.

RDMIXT - This subroutine reads the mixing table data arrays from the scratch data file and loads them into the storage arrays.

I i

l

{

~

7- m g y , y,y 4 , g,- -- ,. me---

Fi l.3.13 l l

Fl1.3 4 4 Nr Data ORNL DWG 83 7030H j l

RDPLOT l

g n > - mm -

O o

c m r m x m" m mm O

m > > 3' > H m o O o RCHRS m > m a t.n-4 n m" m m 0 >

EO mm Fig. Fil.3 8. Flow chart for reading plot data This section of the program reads the plot or picture data used to generate printer plot maps of the mixtures, units and/or bias ID's used in the problem. The plot input data block is described in Sect. Fil.4.ll.

RDPLOT- This subroutine uses MOVE to initialize the plot title to the problem title and the table of characters to the default values. CLEAR is called to initialize the data arrays. MOVE is also used to save data to be used in multiple plots. RCilRS is used to read the plot title and the character string of symbols to be used in the plot. AREAD, IREAD and FREAD are used to read the plot or picture input data. SQRT is used to determine tbc normalization factor for the direction cosines and 10 is called to load the plot data on ine scratch data file.

RCilRS - This subroutine is used to read the plot title and the character string that defines the sym-bols to be used in the plot. GETPTR is used to return the current pointer in the input buffer. RETPTR resets the pointer. AREAD is used ti' read the input data and RCRDLN sets the length of the input buffer. STOP is calla to wnte an error message if the plot title is too long and terminate the problem.-

l

_ =_. . . .

Fi l.3.14 l

Fi1.3.4.5 Biasing Data ORNL -DWG 80-19240R3 R DBI AS y, n -

mx" mm O WAITIN

> 2, >

oO O b  ?

m Fig. Fl1.3.9. Flow chart for reading biasing data This section of the program reads the biasing data used ir the problem. The blasing input data blxk is described in Sect. Fil.4.7.

RDBI AS - This subroutine is responsible for reading the blasing data block and writing it on the scratch data file. AREAD is used to read the keywords used in the biasing data and a title for the biasing material if the energy and space dependent values of the biasing func.

tion are entered from cards. IREAD and FREAD are used to read the numerical data.

Pointers for the storage arrays needed to process the biasing data are determined and WAITIN is called to load the data from the scratch data file into the storage arrays and write them on the direct access data file.

WAITIN - This subroutine reads the biasing data block from the scratch data file and loads it into the storage arrays. 10 is used to load the energy and space dependent biasing function (wiarg) into the storage arrays. RITE is used to write the biasing data on the direct access data file.

Fi l.3.15 FII.3.4.6 Restart Data l ORNL-DWG 8019737 H 1

RDRST 6 a RDALB RDWTS m

i r

O nm 6 m RDARA qam RDICE a m

y x

5 2 692

1. m m

m Fig. Fil 3.10. Flow chart for reading restart data This section of the program reads restart information from the restart data file.

RDRST- This subroutine is called only if the problem is to use data from the restart data file. The program recognizes that restart data will be read if the restart unit is defined as a number -

greater than zero. 10 is used to load the array that contains the 1 D ID's from the re-start data file. Each type of data is loaded from the restart data file using 10 and is writ.

ten on the direct access data file by RITE. All restart data except the mixed cross-section data, the differential albedo data, the array data, and the biasing data are pro-cessed directly in RDRST. RDICE is called to load the cross-section data on the direct access data file, RDALD is called to load the differential albedo data on the direct access data file, RDARA is called to load the array data on the direct access data file, and RDWTS is called to load the biasing data on the direct access data file.

RDAL13- This subroutine is called from RDRST to read the albedo data block from the restart data file and write it on the direct access data file.10 is used to load the albedo pointer and length arrays into memory from the restart data file. CLEAR is called to zero the albedo pointer and length arrays and RITE writes them on the direct access data file.

Each record of albedo data is read from the restart data file, loaded into rm.nory using 10, and written on the direct access data file using RITE. When all the records of albedo data have been processed, the updated pointer and length arrays are rewritten over the initial ones using RITE,

Fi l.3.16 RDICE . This subroutine is called from RDRST to read the crou section data blod from the re-start data file and write it on the direct access data file. CLEAR is called to zero the pointer and length arrays. The length array is then rea$ from the restart data file. RITE is used to write the pointer array and the length array on the direct access data file.

Then 10 and RITE are used to load the cross section data from the restart data file and -

write them on the diiect access data filc. This procedure is repeated for every record of each mixture. The updated pointer and length arrays are then rewritten over the initial ones using RITE.

RDARA- This subroutine is called from RDRST to read the array data block from the restart data file and write it on the direct access data file.10 is used to load the data from the restart data file and RITE is used to write them on the direct access data file.

RDWTS - This subroutine is called from RDRST to read the biasing data bhxk from the restart data file and write it on the direct access data file.10 is used to load the data from the restart data file and RITE is used to write them on the direct access data file.

Yl1.3.4.1 Generate Remaining Data ORNL-DWG 8019238R2 FLDATA m m o m SORTA q p. SORTR WATES m 3 a m S

m mo RGUSED DIFALB $Mbba mo <m g C7 07 m p ALBRD w

HOLE LOCBOX l .

ALBUSE 1

9' $ l m O m m

m LSCAN LODRGC 3 A m

Fig. Fi1.3.11. Flow chart for generating remaining data i

1 Fi l.3.17 TM: sea vi of the program is responsible for generating data 'olocks that are required to solve a peoblem but are act entered directly as data.  ;

FLDATA - The library routine REED is used to load data arrays from the beginning of the mixtures umi en tbc geometry through the geometry data. SORTA is calleo to determine which atrap and holes are used as udl as the array and hole nesting levels. RITE is called to write ~.he geometry data on the direct access data fi!c. RGUSED is called to determine

• hkh geometry regions are used in the problem. SORTR is calkd to generate the mix-it,rc coa:spondence arrey. f t is called again to generate the bias region correspondence arrcy. Th.se correspondeno straya are u$cd to avoid storing mixture cross se:tions and biasing cata ' hat were entered as data but are not actually used in the problem. If boundary conditions specify differattial albedo dau .md they are not avaibble from the

^

restar; data flic, DWA) B is c4hed to read the albedo dats bloch and load the requested data on the direct s:cest ille. If the requested biasing data were unavailable from the .j restart data file, WATI'.S is called to load the energy and position biasing function (wsavg array) on ;he direct access data file.

SORTA - This subroutine checks to see that the global array is properly defined. It determines the -

array correspondence array and the nesting levels for holes and arrays. SORTA uses CLEAR to initialize arrays. REED is used to load the array data and STOP is used to wcite an erwr message and terminate if more computer storage is needed for the problem.

HOLE- This subroutine is called from SORTA to determine what holes occur at the next nesting level and to adjust the array nesting level for arrays that occur in holes. It also checks to be sure holes are not recursively nested.

L O C l3 0 X - This function subprogram is called from SORTA to determine the unit or box type at a given position in the unit crkntation array.

RGUSED- This subroutine determines which geometry regions are used in the problem. The library routine CLEAR is called to zero the space for the region correspondence array LSCAN determines if a particular unit or box type has been used in the unit orientation array and if it-has, LODRGC is called to load the region number into the region correspondence array.

LSCAN - This is a logical function that returns a value of true if the specified unit or box type is used in the unit orientation array. A value of false is returned if the unit or box type was not used in the unit orientation array.

LODRGC This subroutine loads the region number in the region correspondence array.

SORTR- This subroutine is called twice from FLDATA to create a mixture correspondcace array and a biasing correspondence array, These correspondence arrays are used to avoid stor-ing mixture cross sections and biasing information that were defined in the input data but were not referenced in the geometry data utilized in the problem. They are also used ~

throughout the code for accessing the proper mixture cross sections and biasing information.

-r 7 --- -

-erv v -- w = ---e- --'e=-----r-*'--'--'*t--r - r=--'-- * *- ' '-m - - - - -

Fi l.3.18 9

DIFAlli - This subroutine is called if differential albedos are specified as a boundary condition but are not available frorn the restart data file. it rewinds the albedo data file, reads the header record and calculates pointers. ALilRD is called to load the albedo data.

A LilR D - This subroutine searches througn the albedo data file to locate the requested albedo name or boundary condition. If it is not found, an error message is written. If it is found, the number of different differential albedos that were requested are tabulated and AL11USE is called.

AlliUSE - This subroutine writes the pointer array on the direct access data file.10 is used to load data from the albedo data file and RITE is used to write the data on the direct access data file. Then the pointer and lengtn arrays are rewritten on the direct access data file.

WATES - This subroutine reu6s the biasing input data block from the direct access data file and reads the KENO V weights library. STOP is called if the computer storare space is too small to contain the energy and position dependent biasing function (wrarg). 10 is used to load the biasing function into a ternporary storage array. If a specific biasing function is to be used, MOVE is called to load it into the wtavg array, if biasing or weighting data are entered from cards, REED is used to load the data into a temporary storage array. If a specific biasing function that was loaded from cards is to be used in the problem, MOVE is called to load it into the wtavg array. When all tbc data have been procused, RITE is called to load the biasing input data on the direct access data file.

RITE is called again to load the wravg array on the direct access data file.

Fil.3.5 CREATE A MIXED CROSS SECTION DATA FILE ORNt.-DWG 13019233R MIXER I

i l s i 3 l o l l n m po O

JLL2 5 z MIXMIX oE m2 MAKTAP o m

O O g y O l '

$ o_

MIXCRS XLNTHS MAKANG g I I o m

-a o SCOOT r-m o

> m m

Fig. Fil.3.12. Flow chart for mixing cross sections

Fi l.3.19 The function of this portion of the program is to utilire the mixing table data and AMPX working format library from the cross-section data file to create a Monte Carlo formatted mixed cross.section data file. This data file has the same forraat as an ICl! mixed ercr.s section MORSE / KENO librar).'

MIXER - This subroutint controls tbc mixing of cross sectiors and the generation of the angles and probabilities to create a Monte Carlo formatted mixed cross section library. First the mixing table is read from the direct access data ille, MIXCRS is called to generate the mixture correspondence array, and JLL2 is called to generate the array that points to the beginning of each group in the triangularized mixture array. XLNTilS is called to calcu-late the number of direct access blocks required for the mixtures and MIXMIX is called to do the mixing. MAKANG is called to generate the angles and probabilities from the mixed cross sections, and MAKTAP is called to write the Monte Carlo formatted mixture t a pe.

MIXCRS - The mixture correspondence array is generated by this subroutine. This array relates the mixture number in the mixing table to the mixture index.

JLL2- This routine generates an array of pointers that point to the beginning location of each energy group in a triangularized mixture transfer array, XLNTilS- This routine computes the number of direct access blocks necessary to hold the rnixtures.

MIXMIX - This subroutine controls the actual mixing of the cross sections. See Sect. Fil.3,12 for a more detailed description of subroutine MIXMIX.

MAKANG This subroutine controls the generation of angles and probabilities. See Sect, Fil.3.13 for a more detailed description of subroutine MAKANO.

M AKTAP Subroutine M AKTAP is used to write a mixed cross section library in a format similar to the ICE Ill Monte Carlo library format. MAKTAP calls SCOOT to compress out zero 1-D cross sections.

SCOOT- This subroutine eliminates 1 D cross sections that are zero in all groups.

_ .- ._ ._ -= - - _ - _ . - - _ _ . _ . - . _ _ _ _ _ . .__ __._ _ ___ ._

FI 1.3.20 Fll.3.5.1 Cross Section Mixing OHNL-DWG 00 19234 MIXMIX l ,

I I I I I I I 2 5Am H NNITL MIX 2D NORM 1D m SUMSCT a ,

I I I i

n x E PRT MlX 5 h MIX 1D MIX 2M CMPRS NORM 20 I

E..f

• b a

Fig. Fil.3.13. Flow chart of mixing operations MIXMIX - This subroutine controls the. actual mixing of the cross sections. It calls PRTMIX to print the mixing table and calls NNITL to initialize the mixtures. It then reads the input AMPX working library, calls MIX 1D to mix the 1 D cross sections, and calls MIX 2D to mix the 2 D arrays. Afte,r all the nuclides selected from the working library have been mixed, the already mixel cross sections may be used as input for further mixing opera.

tions using MIXID to traix the I-D cross sections and MIX 2M to mix the 2 D cross sec.

tions. NORMID is then called to normalize the fission spectrum and to prepare the adjoint production cross sections if necessary. CMPRS is called to generate the magic word array and to cornpress the 2 D arrays. SUMSCT is called to sum the transfer array by group and NORM 2D is called to convert the transfer array to a probability density function.

PRTMIX - This subroutine prints the requested number of scattering angles and the mixing table. '

NNITL - This subroutine initializes the mixture cross sections to zero on the direct access storage.

MIXID - This subroutine mixes the 1 D cross sections, it mixes most 1 D cross sections using number densities, but the fission spectrum is mixed based on uIf &dE for the nuclide .

being mixed. The flux is the flux used to generate the multigroup cross sections, if it is available. Otherwise a flat flux is used. If the problem is an adjoint case, MIX 1D prepares the cross sections in adjoint form as they are mixed.

MIX 2D - This subroutine mixes the 2-D cross sections from a working library. The mixture cross sections are stored in a triangularized array, if the problem is an adjoint case, MIX 2D-prepares the cross sections in adjoint form as they are mixed.

MIX 2M - This subroutine mixes previously mixed 2 D cross sections into new mixtures using new number densities or volume fractions.

Fi 1.3.21 NORMID - This subroutine is used to normalire the fission spectrum vector, if the problem is an adjoint problem,it also interchanges the fission spectrum and s2p CMPRS - This subroutine compresses out zeros in the 2.D mixture arrays and generates the pointer array used to access data in these arrays.

SUMSCT - This subroutine is used to sum the transfers for each group.

NORM 2D - This subroutine normalites the transfer arrays and divides the P arrays by (2 + 1).

l d Yl13.5.2 Generate Angles and Probabililles ORNL-DWG 80 19735 MAKANG I I I I n a v) o Emo

>cm PRANG E m x g

I l 1 m ' l x GETMUS ANG l.E S BADMOM h I

LEGEND 0 FIND I

Q Fig. Fil.3.14. Flow chart of angle and probability generatioa MAKANG This subroutine controls the generation of angles and probabilities. If the available stor-age is insufficient to generate all the angles and probabilities for one mixture at a time, MAKANG supergroups the data. Subroutine PRANG is called to actually generate the angles and probabilities for a superFroup.

, ~ _ _ _

Fil.3.22 PRANG. This subroutine reads the mixture data for a supergroup and loops through each transfer in the supergroup. It calls LEGEND to convert the legendre expansion to moments.

GETMUS is called to generate the orthogonal polynomials and ANGLES is called to generate the angles and probabilities. If there is an error, IIADMOM is called to print the data input and the data corresponding to the angles and probabilities actually used.

LEGEND This subroutine determines the moments of a function from a Legendre expansion of the function.

GETMUS This subroutine calculates the y,*s and a,'s that determine the orthogonal polynomials, the Q,'s.2 A NGLES - This subroutine determines the angles and probabilities from the 0, polynomials.2 It calls FIND to determine the roots of G,, and calls the function Q to evaluate 0,,

FIND - This subroutine finds the roots of a polynomial G, by using an interval halving technique.

Q- This function evaluates a polynomial Q, by using the recursion formulas.

O,.i(x )=(x us. )O,(x ) alG,-i( A ),

Go(x)= 1.0,and Gi(x)=x #p ilADMOM This routine is called when an error is detected in generating the angles and probabilities.

IIADMOM prints the Legendre coefficients that were input to the calculation and the moments corresponding to these coefficients. It then computes the moments correspond.

ing to the angles and probabilities actually generated and the Legeridre coefficients corresponding to these moments. IIADMOM then prints these moments and coefficients so they may be compared with the original moments and coefficients.

Fil.3.6 WRITE CROSS SECFIONS ON DIRECT ACCESS FILE ORNL-DWG 8019230R2 ICEMIX RDTAPE I

UhOdO m mmm XSECID

-t z >

0D Fig. Fi1.3.15. Flow chart of mixed cross section processing

.- .- .. - - _ ~ = .. - .__-_ .. .

Fi l.3.23 This section of the program is responsible for reading the Monte Carlo mixed cross section library, selecting the desired information, and writing it on the direct access data file.

ICEMIX - This subroutine reads informaton from the Monte Carlo mixed cross-section library, per-forms preliminary checks for data consistency, calculates pointers for the desired data arrays and calls RDTAPE to actually read the library and write the desired information on the direct access data file. i RDTAPE- This subroutine reads the Mc.nte Carlo formatted mixed cross section library, sorts out the data r: ceded by KENO V, and writes the data on the direct access data file. The library routine SQRT is used in calculating the inverse velocities used by KENO V.

The library routine 10 is used repeatedly to read and load data from the Monte Carlo formatted mixed cross section library. RITE is used to write data required by KENO V on the direct access data file. XTENDA is a library routine that is called to extend the number of blocks for a direct access device if too few bkicks were initialized. XSECID is called to process the 1.D cross sections. RDTAPE manipulates the pointer array and writes it on the direct access data file. The Po cross sections, angles and probabilities are also processed by RDTAPE.

XSECI D - This subroutine sorts the 1 D cross sections and loads them in the following order: total-cross section, scattering crow section, production cross section, absorption cross section, extra cross sections for special purposes, and the fission spectrum. The extra cross sec-tions requite tne user to provide programming to utilize them, if one of the required cross sections is not found, it is padded with zeros. The cross sections are normalized by the total cross section and the fission spectrum is summed and normalized to 1.0. The data are transferred back to RDTAPE where they are written on the direct access data '

file, ,

Fil.3.7 WRITE INPLTT DATA ON RESTART FILE ORNL-DWG BO 19231R WRTRST I

l l l l l l l 6 WRTARA WRTALB WRTICE WRTWTS 6 o I i l l- 1 i 3 1 5 A 5 g 5 g 6 g m m m m o o o D-Fig. Fil,3.16. Flow chart for writing data on the restart data file

.- ~ -- -- - - _ _ - , - - . _ - - - - - - - -- . -- .

Fi l.3.24 This section of the program is responsible for writing all data except the calculated results on the restart data file. This section of the program is omitted if a unit number has not been assigned for the restart data file. This information is entered as parameter data, WRS , as described in Sect. Fil.5.3.

The calculated results are written on the restart data nie later in the program. The restart data file is used for testarting a problern.

WRTRST This subroutine writes the input data on the restart data file. The array that contains the ID's of the I.D cross sections is written first. The Feometry data, mixing table data, start data, and energy and inverse velocities are also written. WRTARA is called to write the array data and unit orientation data WRTALB is called to write the albedo data, WRTICE is called to write the cross section data, and WRTWTS is called to write the biasing data.

WRTARA This subroutine is called from WRTRST to write the array number, array size and corresponding unit orientation array on the restart data file for each array that is entered in the problem. The library routine REED is used to read the data from the direct access data file and 10 is used to write it on the restart data file.

WRTAlli - This subroutine is called from WRTRST to write the albedo data on the restert data file.

The library routine REED is used to read the albedo data from the direct access data file and 10 is used to write it on the restart data file.

WRTICE - This subroutine is called from WRTRST to write the cross section data block on the re-start dats file. The library routine REED is used to read the cross.section information from the direct access data file and 10 is used to write it on the restart data file.

WRTWTS This subroutine is called from WRTRST to write the biasing input data block on the re-start data file. The library routine REED is used to read the data block from the direct access data file and 10 is used to write it on the restart data file.

Fil,3.8 GENERATE ALilEDO CROSS SECTION CORRESPONDENCE TABLES ORNL-DWG 80-19232 CORRE I I I I AP# 2 5

8[8 R ATIO Fig. Fil.3.17. Flow chart for generating correspondence arrays

- ..u __ _ - -

_ - _ . _ - ~ - - . - - . - . - . - . .- -. - __.

9 Fi l.3.25 This section of the program generates the correspondence tables that are necessury to correlate the energy group structures of the cross sections and albedos, it is invoked only if differential albedos are used in the problem. j i

CORRE+ This subroutine is called only if differential a;bedos are used. The library routine i CLEAR is used to initialize the strays. CORRE reads the energy bounds for the albedos and the cross sections and converts them to lethargies by using the library routine ALOO. ,

RATIO is called to create a probability array relating the cross-section energy bounds to

• those of the albedos. A second callis made to RATIO to create and print the probability array relating the albedo energy bounds to those of the cross sections. RITE is used to  :

write the correspondence tables on the direct accesa data file, a:

RATIO - This subroutine generates the pointer array that is used to access the albedo data, it also l generates probability arrays that are used to correlate the cross-section energy group structure with the albedo energy group structure. .

Fil.3.9 GENERATE SUPERGROUPED DATA ORNL-DWG 8019243R i NSUPG I

I I I I 1 I l  :

I 2 o Q pp m

POINT IXALB g FILLSG o y

a 7 ,

O

>- y- -r PRTXS RTADJ LIM LN I I v -

8 IXALB ,

s:

Fig. Fil.3.18. Flow chart of super group creation The function of this section_ of the program is to create;supergrouped data from the energy.

dependent input data, it determines which energy group has the largest amount of data associated with -

it, and determines how many supergroups must be created to be able to fit the data into the available computer memory.. The energy groups associated with each supergroup are tabulated and supergrouped data are written on the direct access supergroup data file, one supergroup at a time.

,. . - . . _ , - - - - _ _ . - . _ . - ~ _ - _ _ . . . . . . _ _ . - . _ . _ _ . - _ . _ . -

F11.3.26 l

NSUPG - This subroutine controls the creation of the supergrouped data a i writes them on the direct access supergroup data file. The library routines RD and REED are used to load the cross-section data and albedo data from the direct access data file. PRTXS is called to print the cross-scetion information as described in Sect. Fil.3.9.l. POINT is called to determine the storage requirements of the nonsupergrouped data and create pointers to access these datai The first portion of the additional information table is printed in the computer output. -RTADJ is th% called to right adjust the albedo boundary condition names. These albedo boundary condition names' are then printed in the additional information table, thus completing the table, if I ufficient space is available, STOP is called to write a message and terminate the problera. A rough estimate of the nr 2r of supergroups is made and an implied loop iterative procedure is used to determine the number of supergroups that must be created to fit the problem in the available space.

IXALB is called to determine the amount of space required for the albedos corresponding to a cross-section energy group. A check is made to be sure the largest amount of data for a single energy group will fit in the available memory, if they will, supergrouping is possible. Otherwise a message is written and a stop is executed. Once the number of ,

supergroups is determined, LIMLN is called to calculate and print information in the-space anc supergroup information table. The printed information includes the supergroup and corresponding energy groups the length of the cross sectik and albedo data for the supergroups and the totallength of each supergroup. FILLSG is then called to construct the supergroi os as described in Sect. Fil.3.9.2.

PRTXS- This subroutine prints the cross section information as described in Sect.. Fil.3.9.1.

POINT - This subroutine determines the storage requirements of the nonsupergrouped data and creates pointers to access data within the nonsupergrouped storage array, RTA0J- This subroutine right adjusts the albedo boundary condition names which are read in as left-adjusted data. RTADJ utilizes the library routine ICOMPA to determine if a char-acter is blank.

IX ALB - This function determines the amount of space necessary to contain the albeco data -

' corresponding to a cross-section energy group.

LIMLN - This subroutine is called to calculate and print the supergroup number, the energy groups contained in the supergroup, the length of the cross section and albalo data in the super-group, and the total length of the supergroup. IXALB is utilized to obtain the amount of space required to contain the albedo dna corresponding to a cross-section energy group.

FILLSG - This subroutine constructs supergroups as described in Sect. Fil.3.9.2.

4

Fil.3.27 F11.3.9.1 Print Macroscopic Cross Sections O R N L- DWG 80 19228 PRTXS I

x m m :o m H b

PRT1DS PRT2DS Fig. FI1.3.19. Flow chart for printing macroscopic cross sections This portiot. of the program prints the macroscopic cross-section data for materials used in the prob-lem description.

PRTXS- If macroscopic cross sections are not to be printed, a return is executed. PRTXS loops over the number of mixtures that are used in the problem. REED is used to load the data, and pointers into the data arrays are calculated, if the space is insufficient to con-tain the data, a message is printed. If I-D mixture cross sections are to be printed, PRTIDS is called to print them. If the extra 1-D cross sections are to be printed, REED is used to load the data and PRT2DS is called to print them. If the number of scattering -

angles is greater than zero and the mixture probabilities and angles are to be printed, REED is used to load probability data and PRT2DS prints them. Then REED loads angle data and PRT2DS prints them.

PRTIDS - This subroutine piints the macroscopic l-D cross sections, one energy group at a time PRT2DS - This subroutine prints a two-dimensional variable length array in a compact manner.

4 m ,

Fil.3.28 Fl1.3.9.2 Write Supergroup Data File

'ORNL-DWG 80-19229 FILLSG

-l i I I I I I ox m m pom SGALB RT q p g. m m i I I x x m _.

FIL2D m o SGWT Q o m I I

.x x '

O O Fig. Fi1.3.20. Fiow chart for loading supergrouped . data This portion of the program collects the group-dependent data by supergroup and writes _them on-the direct access supergroup data file.

FILLSG - This subroutine is responsible for filling the supergroups and writing them on the direct access supergroup data file. For each supergroup, CLEAR is called to initialize the work-ing space. Pointers are calculated for the data arrays and space is allotted for the calcu-lated data such as fluxes that will be supergrouped. The library romines REED and RD are used to load data from the direct access data file into the proper arrays as follows:

For each mixture the inverse velocities are loaded, followed by the pointer array and all the 1-D cross-section arrays. RD and REED are used to load the 2 D arrays from the --

direct access data file, FIL2D is called to load them into the' supergroup._ Pointers are calculated for the albedo data and SGALB is called to load the albedo data-into the supergroup. ' SGWT loads the average weight array (biasing data) into the supergroup.

FILLSG then calls RT to write the calculated data for the supergroup Lon the_ direct' access supergroup data file. RITE writes the group-dependent data on the direct access supergroup data file.

FIL2D - This subroutine loops over the number of mixtures. It uses RD to load the-2 D cross -

~

section data for the supergrc up from the direct access data file; first the Po data, then for each scattering angle, the angles and probabilities. The pointer array is redefined so the supergrouped data can be accessed.

SGALB- This subroutine uses REED and RD to load the albedo data for the supergroup'from the direct access data file.11t loops over the number of differential > albedos used in the -

problem.' Then the pointer array is redefined so the supergrouped data can be accessed.-

SGWT .- This subroutine loops over the number of biasing regions used in the problem. RD is used

- to load the average weight array from the direct access data file. If any_ average ~ weight-entry remains undefined or zero, it is set to the default value of weight average.

a -, . . , , ..au -.-. . - . - - . - . = . . .

._. . .m.. - .. . - . _ _ _ _ _. ._ _- _ -. . . -

i 1 ;. -

Fi l.3.29 RT- This subroutine is called to write the calculated data'(fluxes, etc.) on the direct access supergroup data file. i RITE - This' library routine is used to write the Froup-dependent data for the supergroup on the direct access supergroup data file.

Fil.3.10 PROCESS GEOMETRY ORN L-DWG 83-7631R JOMITY LOADIT h CORSIZ PRTJOM ARALBA JOMCHK l 8

o z o PnTLBA VOLUME AflASIZ l$

x I F

-n O

O m

LSCAN-3 Fig. Fil.3.21. Flow chart for processing geometry _

This portion of the program is primarily responsible for loading the geometry data, generating addi -

L tional geometry data, checking the geometry for consistency, writing;crror messages related to the -

geometry, and printing the geometry that is used in the problem.-

i. JOMITY - This subroutine is responsible for generating additional geometry data, checking the l- geometry data, writing geometry error messages, and printing the geometry.

l^

L LOADIT - . This subroutine loads the geometry data and the non-supergrouped portion of.the albedos data.' Section Fil.3.10.1 contains a more detailed description of the procedure.

CORSIZ -- This subroutine sends the appropriate lattice or array information to ARASIZ for each :

lattice that is used in the problem. Using this information, it calculates the overall post-tive dimensions of the global array. The library routine, SQRT, is utilized to calculate the maximum chord length of an unrcilected array, a reflected array or a single unit-problem

. . . .-a w.- - ..-. .:.-.~ -.. = .. :. ..--- .~ x .. - ,..- .-. . . - ..--

- . . . .. -.. .-. ~ - . - . - .

4 F11.3.30 ,

ARASIZ - This subroutine uses the array unit orientation data to calculate the positive dimensions of -

'the core boundary for that array or lattice. The function LSCAN is called to determine if a specified unit or box type has been used in the array. ARASIZE also checks to assure that the faces of adjacent units are the same size and shape. Several error mes-

. sages are written if errors are encountered.

LSCAN - This is a logical function that returns a value of true if the specified unit or box type is used in the unit orientation array. A value of false is returned if the unit or box type was

- not used in the unit orientation array.

PRTJOM - This subroutine prints the Feometry data that are used in the problem.

ARALBA - This subroutine calls PRTLBA for each array that is used in the problem.

. PRTLBA - This subroutine is called to print the unit orientation data for_cach lattice or array that is-used in the problem. It prints the error and/or warning messages associated with each-lattice. STOP is called if a unit or box type number exceeds 10,000.

JOMCilK - The purpose of this subroutine is to perform consistency checks on the geometry data and write the appropriate error messages. See Sect. Fil.3.10.2 for additional details.

VOLUME This subroutine i: responsible for calculating the volume of each geometry region _and the cumulative volumes for each unit that is used in the problem. See Sect. Fil.3.10.3 for additional details.

4 i

, . ~ . . . . . - , ~ . . , . . , _ - . _ . , , . _ . . , ..a..

Fl 1.3.31 Fi1.3.10.1 Load Data From the Direct Access File

-GRNL-DWG 8019224 R LOADIT LODARA PRTARA LODALB a

o m m

I m

g BOXC

> c o

n HOLE LOCBOX h .

P m

o o

m Fig. Fi1.3.22. Flow chart for loading data from direct access This portion of the program loads data from the direct access data file into permanent memory.

LOADIT - This subroutine calls the library routine REED to load the geometry data. If the problem is an array problem (lattice geometry)- LODARA is called to load the lattices that are used in the problem and recompute and readjust the array nesting level array and hole nesting level array. If multiple boxes are used in the prob' n. PRTARA is called to print the unit orientation array for each lattice used in the problem. BOXC is called to load the box correspondence array and LODALB is called to load the non supergrouped por-tion of the albedo data. ,

LODARA - This subroutine is responsible for loading the lattices (unit orientation arrays) that are used in the problem, computing the hole nesting level array, and computing and adjusting the array nesting level array. CLEAR is used to. initialize the arrays and REED is used-to load the unit orientation arrays, ilOLE and LOCBOX are both called by LODARA.

HOLE- This subroutine is called from LODARA to determine which holes occur at the next nest-ing level and to adjust the array nesting level for arrays that occur in holes. It also checks to assure that holes are not recursively nested. CLEAR is used for initialization purposes and STOP is called if holes are recursively nested.

, a.. . __ .- _ _ . - . . _ . _ _ - _ .

Fil.3.32 LOCBOX This' function is called from LODARA to return the unit or box type at a given position in the unit orientation array .

PRTARA This subroutine prints the unit orientation array for each lattice that is used in the problem.

BOXC- This subroutine uses the number of units or box types and the geometry region _ number -

corresponding to the first and last geometry region of each unit to generate the box corre-spondence array which contains the unit or box type number for each geometry region.

This is loaded in the appropriate position as it is generated.

I' LODALB- This subroutine calls the library routine REED to load the pointer and length arrays for -

the albedo data from the direct access ' data file. _ REED is used to load the nonsuper-grouped albedo data, for each albedo that is used, into a temporary array. A loop over the number of angles is then used to load these data into the appropriate' arrays. When all of the albedos used in the problem have been processed, REED is called to_ load the pointer arrays for the cross sections and albedos as well as the arrays defining the albedo to cross-section energy group correlation.

f d.

5

--'r- cNo m, -v e , , ,, ,, ~ e,-~, w-s

l Fi 1.3.33 Fl1.3.10.2 Check the Geometry Data ORNL-DWG 8019226R2 -

JOMCHK XXLIM CRMAX HOLCHK SRMAX i

m i f 1r o

o

-d ADJUST HOLEXT HOLHOL I

E O  ;

< n m I XXLIM SRMAX CRMIN SRMIN 1 r' 1r i f CRMAX XXMIN XRMIN.

I f m m O O I :o :D H H i

n Fig. Fi1.3.22 Flow chart of geometry checking procedure This portion of the program checks the geometry for inconsistencies, surface intersections, and other errors.

JOMCHK - This subroutine checks each geometry region to assure that it does not intersect the next L outer region.- If an intersec: ion occurs, an error flag is set 'and an error message is writ-ten. JOMCHK checks each surface of the outer region for an intersection. If the surface -

is a planar surface. XXLIM is used to return the farthermost point of the inner region in -

the direction of the plane specified in the call (i.e., for the -x face, XXLIM returns the -

most negative x value of the inner region).~ For a spherical surface, SRMAX is used to return the length of the maximum radius vector of the inner region with respect to the origin of the outer region. - For a cylindrical surface, CRMAX is used to return the length of the maximum radius vector of the inner region with respect to the axis of the outer region.

e Fi1.3.34 -

l CRMAX . - This function determines the maximum cylindrical radius vector of a geometry region with respect to a given axis, and then returns the magnitude of that vector. See Sect. F1i.3.10.2.1 for additional details.

XXLIM - This routine returns the maximum coordinate of an interior region ' corresponding to a par-ticular face direction (for negative face directions maximum means most negative).

SRMAX - This function determines the maximum radius vector of a geometry region with respect to a given origin, and then returns the magnitude of that vector. See Sect. Fil.3.10.2.1 for additional details.

HOLLi!K This subroutine is responsible for assuring that a hole doesn't intersect any other geome-try region. ADJUST is called to adjust the dimensions of the hole with respect to the ori-gin of the unit that contains the hole. HOLEXT is called to check for a hole intersecting the region external to it. HOLHOL is used to check for a hole intersecting the region internal to the region that contains the hole, it is also used for checking for the intersec-tion of two holes.

ADJUST - This subroutine corrects the dimensions of a region represented as a hole, with respect to the origin of the unit that contains the hole.

HOLEXT- This subroutine checks for a hole intersecting the region external to it. XXLIM is used to return the farthermost point of the hole in the direction of the plane specified in the call. CRMAX is used for a cylindrical surface to return the length of the maximum radius vector of the hole with respect to the axis of the outer region. SRMAX is used for a spherical surface to return the length of the maximum radius vector of the hole with respect to the outer region.

HOLHOL - This subroutine is responsible for assuring that a hole doesn't intersect the geometry region internal to the region that contains the hole. It also checks far holes intersecting each other. XXMIN is used to return the nearest point of the hole in the direction'of the plane specified in the call. CRMIN is used for a cylindrical surface to return the length of the minimum radius vector of the hole with respect to the axis of the outer region.

XRMIN determines the minimum coordinate of a hole with respect to a flat circular face.

SRMIN is used for a spherical surface to return the length of the minimum radius vector of the hole with respect to the region being checked for an intersection.

XXMIN - This function returns the minimum coordinate of the hole with respect to the face of the cuboid specified in the call. SQRT is utilized in determining the minimum coordinate of spherical or cylindrical holes.

CRMIN - This function returns the magnitude of the minimum cylindrical radius vector of a hole with respect to a given axis. See Sect. Fil.3.10.2.1 for additional details.

XRMIN - This function dete-mines the minimum coordinate of a hole with respect to a flat circular face. SQRT is used in processing spherical and cylindrical holes.

SRMIN - This function returns the magnitude of the minimum radius vector from the center of a sphere to another geometry region. See Sect. Fi1.3.10.2.1 for additional details.

-l

F1 L3.37 This portion of the program is responsible for calculating the volume of each region used in the problem, the cumulative volumes for each unit used in the problem, the number of times each unit was _

used in the problem, and the total volume of each region summed over all occurrences.

_ VOLUME . This subroutine calculates the volume of each region for every unit that is used in the problem. It then calculates the cumulative volumes for each unit. CLEAR is used to ini-tialize arrays. If an external reflector is present,-IlUNTER is called to determine the number of times cach array and/or hole is used in the reflector. GOCURS is used to__

determine the number of times each unit, array and hole is used in the problem.

GTVOLS is called to calculate and print the number of occurrences for each unit and the corresponding total volumes for the entire system.

l{UNTER - This subroutine determines the number of times each unit, array and hole is used.

CLEAR is used to initialize storage arrays for the present hole level and the next hole level. MOVE is used to move the storage arrays.

GOCURS- This subroutine loops over the array size and calls llUNTER to determine the number of times each unit, lattice or array, and hole is used in the problem.

GTVOLS - This subroutine calculates the total volume of each region for the entire problem by mul-tiplying the volume of the region by the number of times the region is used in- the problem.

Fil.3.Il LOAD BIASING OR WElGIITING DATA ORNL-DWG 8019225R2 LODWTS I

I I I I m n 2 ypC PRTWTS o>:o Fig. Fil.3.26. Flow chart for loading biasing data This portion of the program is executed only if the input panameter data contain PWT-YES, as described in Sect. Fil.4.3. If biasing data are to be printed, the program loads and prints the average weight array.

. F11.3.38 LODWTS JThis subroutine is responsible for printing the bias ID's versus the material ID's used i the problem and for_ loading and printing the biasing or weighting data. The number of sets of data that .will fit in the available memory is calculated. . Then the library routine CLEAR is used to initialize that space. .RD is.used to load the data.that will fit and PRTWTS is called to print it.. Then the entire process is repeated until_all the biasing or -

weighting data used in the problem have been loaded and printed.

PRTWTS - This subroutine prints the group-dependent,veight average _ array for each biasing region in a compact fashion.-

4 Fil.3.12 GENERATE PRINTER PLOT d

ORNL-DWG 83 7634 PRTPLT I

m PRINT o

l MESH RELATE 1: 1-o UNTCRS g LOCATE 1 =

P I l l m

$ POSIT $ FINDBX LOCBOX

-m Fig. Fil.3.27. Flow chart for pictures or plots - '

This portion of the program generates printer plots of a two-dimensional slice through the geometry.

As many plots as are desired can be printed.

PRTPLT - This subroutine controls the generation of the printer plots. If the plot is specified to

' print by unit numbers, subroutine UNTCRS is called to generate a unit correspondence array, REED is used to load the picture data from direct access. The-picture title is printed and subroutine RELATE is called to print a heading for the symbol map and print the symbol map._ The picture coordinates, direction cosines and number of symbols across and down the page as well as *.he step intervals are printed. Then subroutine PRINT is called to generate the actual picture.

Fi1.3.35 4

Fl f,3.10.2 l Determine Distances okNL-t)WG 81 7637 CRMAX _6RMAX l -

I

.. m m gg m .,

DOT?RD 'ECNRM y t

g CRSPRD VECADD C RSF A D VECADD DOTPRD VECNRM CRVIN SRMIN II II O$ CRSPRD VECDif b CRSPR D VE CDIF

%$ %5 DOTPRD VECNRM VECADD DOTPRD VECNRM VECAOD Fig. Fil.3.24. Flow chart for distance to intersection This section of the geometry checking procedure is utilized in checking for geometry surface intersections.

• CRMAX- This function determines the maximum cylindrical radius vector of a geometry region with respect to a given axis, and then returns the magnitude of that vector. Depending on the geometry type, CRM AX may call CRSPRD to generate the cross pmduct of two vec-tors, DOTPRD to generate the dot product of two vectors, VECADD to add two vectors together and VECNRM to multiply a vector by a scalar. STOP is called if geometry inconsistencies are encountered.

SRM AX - This function determines the maximum radius vector of a geometry region with respect to a given origin, and then returns the magnitude of that vector. Depending on the geome-try type, SRM AX may call CRSPRD to take the cross product of two vectors, DOTPRD.

to take the dot product of two vectors. VECADD to add two vectors together, and VECNRM to multiply a vector l'y a scalar. STOP is called if geometry inconsistencies are encountered.

Fi l.3.36 CRMIN + This function determines the minimum cylindrical radius vector of a geometry region ith respect to a given axis and returns the magnitude of that vector, The geometry type determines which functions will be used to calculate the minimum radius vector, DOTPRD is used to generate the dot product of two vectors, CRSPRD generates the -

cross product of two vectors, VECNRM multiplies a vector by a scalar, VECDIF subtracts two vectors, and VECADD adds two vectors together, STOP is called if geome-try inconsistencies are encountered.

SRMIN - This function determines the minimum radius vector of a geometry region with respt to a given origin (center of a sphere) and returns the magnitude of that vector. Depending on the geometry type, SRMIN may call DOTPRD to take the dot product of two vectors, CRSPRD to take the cross product of two vectors, VECNRM to multiply a vector by a scalar. VECDIF to subtract two vectors, and VECADD to add two vectors. STOP is called if eometry P inconsistencies are encountered.

CRSPRD - This is a utility routine to generate the cross product of two vectors.

DOTPRD - This function returns the dot product of two vectors.

VECADD- This subroutine returns the result of adding two vectors.

VECNRM - This routine scales a vector by a constant.

VECDIF - This subroutine returns the difference of two vectors.

Yl1.3.10.3 Calculate Volumes ORNL-DWG 83 7633R VOLUME I

I I I I I I I

$ O h m

HUNTER h GOCURS GTVOLS m m 4 E b

• l l 9m

$ HUNTER E I I o  :

F m o Fig. FI1.3.25. Flow chart for calculating volumes ,

Fi l.3.39 PRINT - This subroutine determines the number of pages that will be needed to print the picture, i Subroutine MES11 is called to load the appropriate mixture numbers, unit numbers or bias ID numbers for each line of print for the picture. Then PRINT prints the line of symbols correspnding to them.

M ES}l - This subroutine loads an array that contains the appropriate mixture numbct, unit num-ber or bias ID number for each character in a line. CLEAR is called to initialize arrays-if nested holes or nested arrays are present in the problem. LOCATE is called to deter-mine the geometry region and unit or box type that contains each mesh point. MESil then loads the mixture number, unit number, or bias ID number.

LOCATE- This subroutine is responsible for determining the geometry region for each mesh point in the picture. If the mesh point is within an array, FINDBX is called to determine the position within the lattice or array that contains the mesh point. LOCBOX is then called to determine the unit or box type that contains the mesh point. POSIT is used to deter, mine the geometry region that contains the mesh point.

FINDBX - This subroutine Iceates the position in an array that contains a specified point.

LOCBOX- This function returns the unit or box type at a given position in an array.

POSIT - This subroutine determines the region within a unit that contains a specified point.

Fil.3.13 PROCESS IllSTORIES BY SUPERGROUP onNi owG no 872?R GUIDE I

i ii e i ai i l l l l l b R$ PS A 22 5

{ g ST ART mm INDX BANKrR g yp NST A RT p WRrCAL

~"

l I l

RDCALC CHKST R l '

RESET TRACK F ISF L X I , f m

$h O w WHTGRP 1r i I l { 1r <r 5

T AKWRT N 8

E l

Fig. Fil.3.28.- Flow chart of tracking routir.es This section of the program is where the tracking of the individual histories is done, one supergroup at a time.

Fil.3.40 GUIDE - This subroutine controls the tracking procedure. It loads the calculated data for a re-started problem, calls subroutine START to obtain the initial source distribution, calls CIIKSTR to load the initial starting distribution in COMMON /NUTRON/ and prints the starting points as requested by the data. The library routine CLEAR is called several times to initialize arrays. IOLEFT and JSTIME are called to initialize the I/O's and time for the tracking procedure. SQRT is used in estimating the lower limit of the 99%

confidence interval of the sample distribution of k-effective.

The heart of subroutine GUIDE is a loop over generations, from the starting genera-tion to the number of generations requested. Subroutine RESET is called to accumulate the fission source and the source vectors for matrix k cffective. it also counts the number of histories in each supergroup and determines the supergroup with the largest number of histories. Then subroutine BANKER is called to sort the histories by supergroup, loading the largest supergroup at the top of the bank. GUIDE calculates pointers for the super-grouped data and loads the supergrouped data using the library routine REED. TRACK is called to do the actual tracking. The library routine RITE writes the calculated super-grouped data on the direct access supergroup data file. When all the supergroups have been processed, NSTART is called to provide the fission source for the next generation.

Then FISFLX is called to calculate matrix information and statistics for the calculated data. GUIDE then checks to be sure sufficient time and I/O's remain to assure that another generation can be processed. If another generation cannot be processed and re-start data are to be written, WRTCAL is called to write the calculated data on the res.

tart data file. A message is printed by GUIDE stating the reason for terminating the calculation.

GUIDE is a very important subroutine in KENO V, The following table is provided to assist in understanding the functions performed by the subrautines called by GUIDE.

SUBROUTINE - FUNCTION CONDITION JSTIME monitor time usage always RDCALC load calculated data for if the problem is restarted restarting a problem REED load data from direct access always -

supergroup data file RD load data from direct access always START provide initial source if the problem is started with the first generation

- CHKSTR print starting points if requested INDX locate cross-section index always RESET count histories / supergroup always BANKER sort the neutron bank always TRACK track individual histories always RITE write data on direct access always NSTART provide fission source for always the next generation FISFLX calculate statistics always IOLEFT monitor I/O usage always PULL terminate problem if excessive time is used WRTCAL write data on restart file if a restart data file is to be created

, - . ~ ~ -

4 Fl 1.3.4 I

- JSTIME - This library routine is called several times from GUIDE for timing purposes.

RDCAl.C - This subroutine is called only if the problem is being restarted at a generation greater than 1. Its purpose is to read data from the restart data file and write the supergrouped data on- the direct access - -data file. See Sect. Fil.113.1 for . additional information.

REED- This library routine is called early in GUIDE if a problem is not being restarted in order -

to load data that are needed to create the initial source distribution. REED is called to load supergrouped data for the supergroup being processed from the direct access super.

group file.

RD- This library routine is called to load the fission spectrum for use in creating the initial source distribution.

START- This subroutine is responsible for creating the initial source distribution. See Sect. Fi1.3.13.2 for additional details.

CilKSTR - This subroutine calls the library routine MOVE to load the initial source distribution into COMMON /NUTRON/. If the starting points are to be printed, TRKWRT is called to print them using the debug tracking format.

TRKWRT This subroutine is called from Cl!KSTR to print information about the current status of the current neutron-in the debug tracking fortrat. When TRKWRT is called from CHKSTR, the information of interest is the position at which the neutron was started.

RNDOUT is called from TRKWRT to make the current random number available for printing.

CLEAR - This library routine is called to initialize the fission density atray and the arrays that hold the matrix k-effective and associated statistics.

INDX - This subroutine is called only if the average number of neutrons per fission and the aver. -

age energy at which fission occurs are to be calculated. (See Sect. Fil.4.3, NUB .)

INDX determines the position of the fission cross section in the extra 1-D cross-section array. The fission cross section is required for calculating the average energy at which fission occurs.

RESET - - This subroutine is called to accumulate the fission source and the source vectors for the-'

matrix k-effective and to count the number of histories in a supergroup, FLANKER - This subroutine is responsible for sorting all the particles in the current supergroup into the top of the neutron bank and all other particles into the bottom of the bank.

TRACK - -This subroutine is responsible for the actual tracking of each individual history. See Secti Fil.3.133 for a detailed description.

Fi 1.3.42 RITE - When the program returns from TRACK, RITE is called to write the calculated super-grouped data on the direct access supergroup data file.

PULL- This library routine is called from GUIDE to set a time interval that results in a nonstan-dard return if that time interval is exceeded. This is for the purpose of preventing the program from looping indefinitely. PULL is called later in GUIDE to reset the time interval as appropriate.

NSTART - This subtoutine is called from GUIDE to provide the fission source for the next genera-tion. See Sect. Fil.3.13.4 for specific details.

FISFLX - This subroutine calculates statistics for k-effective, the matrix k-effective, fissions, absorp-tions, leakages, and fluxes. Section Fil.3.13.5 contains additional details.

lOLEFT - This library routine is called to determine if sufficient 1/O's remain to allow processing another generation.

WRTCAL - If a restart data file is to be created, this subroutine writes the calculated information on the restart data file with a frequency specified by the parameter data (Sect. Fil.4.3, RES ). RNDOUT is called to preserve the random number. Then the generation number, random number, number of histories per generation, number of energy gtoups, banked information, some common information and all the k-effectives calculated to this point are written on the restart data file. The neutron bank and, if requested, the fission densities are written. If matrix k-effective information is requested,10 is used to write it on the restart data file. Then WRTCAL loops over the number of supergroups, calculat-ing pointers, using REED to load data from the direct access supergroup file and calling WRTGRP to write the group-dependent calculated information on the restart data fi:e.

When all the data have been written, a message is printed.

WRTGRP - This subroutine writes calculSted data (leakages, absorptions, fissions, and if requested, fluxes) for each energy group on the restart data file.

Fi1.3.13.1 Load Calculated Rutart Data ORNL-DWG 80 19223 RDCALC i i I

!U km 9

Z RDGRP Fig. Fi1.3.29. Flow chart for loaaing calculated restart data

... .. ~ . . . - - . .

Fi l','3.4 3 4

This sect _lon of the program loads the calculated data such as k effectives and fluxes from the restart data file if the starting generation number is ym.ict than 1.

RDCALC . This subroutine is called from GUIDE if the starting generation number is greater than 1.

This indicates that a calculation is to be restarted using the starting generation number as the first generation to be processed. Thus all the results that were calculated in a previ.

ous run must be loaded from the restart data file to continue the calculation. RDCALC reads the previously calculated data from the restart data file and checks for consistency against parameters that were entered as input data. Appropriate messages are printed if

-inconsistencies are encountered. - RNDIN may be called to load a new random number.

10 is used to load data from the restart data file. Pointers are calculated for the super-grouped restart data and RDGRP is called to read the group-dependent data from the restart data file. RITE is used to write the restart data on the supergroup data file.

RNDIN - This libra y routine is called to load a new random number for use with the restarted problem if a random number was entered in the parameter input data.

10 - This library routine is used to load matrix k-effective information if it is to be calculated.

RDGRP- This subroutine is used to load the supergrouped data from the restart data file. This includes leakages, fissions, absorptions and fluxes.

RITE - This library routine is used to write previously calculated results on the direct access supergroup data file so the problem can be restarted properly.-

F11.3.13.2 Generate initial Source Distribution -

om owt so tema; s1 ART I I I I l l 1  : a i i STARTO ST A RT 1 LOC 80x $Ta n f 4 ST A R TS START 6 ST RTSU START 3 f VOL'!S l l START CMOO55 CHOOSE f LOCATE I i

• i

$iks$A$ ' 'i 5 Ej!"5SE '

i 1 I

, , l ROstt l { l moex l LocsOx l START 5 ST A R71 i ji 1 5i Fig. F11.3.30. - Flow chart for providing initial source distribution This portion of the program is responsible for generating the initial source distribution in accordance with information specified in the start data (see Sect. Fil.4.8).

= _-. . ._ _

F11.3.44 -

START- 'This subroutine is responsible for generating the initial source distribution. If fissile material is not used in the problem STOP is called to write a message and terminate the problem. Appropriate messages are printed if the specified start type is incompatible with the geometry configuration. Subroutine VOLFIS is called to calculate the volume fraction of fissile material. Then START 0, STRTSU, START 1, START 2, START 3, START 4, STARTS, or START 6 is called to generate starting points having the charac-teristics specified in the start data (see Sect. Fil.4.8). Subroutine LOCBOX is calkd after both START 2 and START 3 to determine the unit number at the specified position in the array. Subroutine LOCATE theti determines the geometry region that contains the specified point by utilizing POSIT, FINDbx and LOCBOX. FINDBX is called to locate the position within the array that contains the starting point. LOCBOX is called to - ,

determine the unit number located at that position in the array.- The starting point is translated to the coordinate system of the unit and POSIT is called to determine which region within the unit contains the starting point. A check is then made to be sure the region contains fissile material. If it does not, the point is discarded. If the region con-tains fissile material, GTISO is called to provide the initial direction cosines. START:

uses FLTRN to set the initial energy group and MOVE is called to load the initial data for the history into the neutron bank. JSTIME is called to be sure the allowed time is not exceeded. If it is, or if the required number of source neutrons have been generated, the starting is terminated, if too few initial soure: neutrons exist, FLTRN and MOVE are used to fill the remaining starting positions ' . a those that were generated. A mes-sage to that effect is then printed.

STOP- This library routine is called from START to write an error message if fissile material is not utilized in the problem description. At least one mixture having a nonzero fission spectrum must be used in the problem description.

VOLFIS -- '1his subroutine determines the volume fraction of fissile material in an unreflected array or an array whose reflector material is not fissile. It determines the volutne fraction of fissile material in the system for single unit problems and reflected problems having fissile reflector material. If the volume fraction of fissile material is found to be zero, an error message is written and execution is terminated.

STARTO - This subroutine is called from START to generate a uniform initial source distribution in a cuboidal volume. This is accomplished by choosing points uniformly throughout the vol-ume by using the library routine FLTRN, and discarding points that do not occur in fis-site material. See Sect. Fil.4.8 and Table Fil.4.6 for assistance in modifying the default boundaries over which the starting points are chosen.

STRTSU - This subroutine is called to generate a uniform initial source distribution for a single unit problem or a reflected problem for which the user has specified that the reflector be included in the starting distribution. FLTRN is used to choose points uniformly through-out a cuboidal volume. AZIRN and FLTRN are used to choose points uniformly throughout a cylindrical or hemicylindrical volume. GTISO and FLTRN are used to choose points uniformly throughout a spherical or hemispherical volume.

AZlRN - This library routine provides the sine and cosine of a random azimuthal angle.

~

GTISO - This library routine provides the direction cosiacs of an isotropically distributed random direction. It is used to generate an isotropic source distribution.

l Fi 1.3.45 STARTl- This subroutine is used to provide starting points chosen from a cosine distribution. l The library routines ARSIN and FLTRN are used to provide the cosine distt;bution, See Table Fil.4.6 for details of the various initial starGng distributk,y ARSIN - This library routine is the arcsine function,'y srcsine(x). and is used in generating a cosine source distribution.

START 2 - This subroutine starts a specified fraction of the initial source distribution uniformly in fissile material in the unit located at a specified position in the global array. The remain-der of the initial source is chosen from a cosine distribution as described in T6ble Fil.4.6.

START 5 is called to determine the source points located in the unit at the specified loca.

tion, and STARTl is called to choose points from a cosine distribution.

7 LOCBOX - This function is called to return the unit or box type at a given position in a given array.  ;

START 3 - This subroutine starts all the initial source neutrons at a specified point within the unit ,

located at a specified position in the global array.

START 4 - In this subroutine, a unit type is specified for starting the initial source distribution. A uniform sampling is made over the global unit orientation array to locate units of the specified type, and start the initial source neutrons at a specified positions within these units. CilOOSE is called to determine the positions within the global array that are occupied by the specified unit type.

CilOOSE This subroutine locates the positions of a specified unit within the global unit orientation array by randomly choosing positions in the array and discarding them if the specified unit was not at that position. The library routine TLTRN is used to randomly choose positions in the unit orientation array, START!- This subroutine starti the initial source neutrons uniformly in fissile material within a specified unit type. A uniform sampling is made over the global unit orientation array to locate units of this type by utilizing subroutine CHOOSE.

START 6- This subroutine starts the initial source neutrons at points specified by the user. These points must be specified relative to the origin of the global array. See Table Fl1.4.6 for exact specifications.

LOCATE- This subroutine determines the geometry region that contains the specified starting point.

FINDBX is used to determine the point's location in an array. LOCBOX determines the -

unit number at that location and POSIT determines the region within the unit.

POSIT - This subroutine determines the region within the unit that contains the specified position.

FINDBX - This subroutine locates the position in an array that contains a specified point.

LOCBOX- This function returns the unit or box type for a specified position in an array.

.- . , - .. . - . - ~ - - . -. -. . - . , _ .

- Fi1.3.46 R

MOVE- This library routine is called from START to load data from COMMON /NUTRON/

into the neutron bank. It is'also used to pad the neutron bank to provide enough starting'.

positions if too few were initially created..

FLTRN - This library routine is called from various subroutines during creation of the initial source distribution, to return a random number between zero and 1. START calls F1.TRN to 1 aid in choosing the initial source neutrons. It is also called if too few starting positions '

were generated. It is used to randomly choose from the initially created starting positions to pad the neutron bank until sufficient starting points exist.

JSTI.J E - This library routine is used for timing purposes.

Fl1.3.13.3 Track Individual Histories ORNL-DWG 8019218R TRACK g m m o m m >-

ALBIN o TRKWRT gX LOCBOX -t

? - @ - t:! ,

1< m m :o i 2 m o o y z g 2 m

LOWRT z CROS ALBED0 o

o C

H -

m- m- p a r- N . -

2 H $ m z

z Fig. F11.3.31. Flow chart for tracking individual histories -

a This section of the program does the actual tracking of the individual histories.

Fl 1.3.47 TRACK- This subroutine is called by GUIDE to accomplish the actual tracking of the individual- i histories. Each history is tracked, and its contributions to the various calculated results are tabulated, until it escapes from the system or is killed via Russian roulette. If a his- ;

tory changes supergroups as a result of a collision or an albedo reflection, it is stored in !

the neutron bank. In the course of tracking a history, an initialization call is made to subroutine ALBIN if differential albedo boundary conditions are utilized in the problem.

LDWRT may be called to print debug information and, if history tracks are to be  !

printed TRKWRT is called from strategic locations throughout TRACK to provide perti- I nent information about the history as it moves through the tracking process. The library routine MOVE is utilized throughout the tracking procedure to move data in and out of storage arrays and commons. FLTRN is used to provide random numbers used in play-ing Russian roulette, processing downscatters, picking fission points, picking scattering-angles and determining the fission energy group. EXPRN provides a random number, selected from an exponential distribution, to be used as the number of mean free paths a history can traverse. CROS is called to determine if a boundary crossing has occurred.

LOCBOX is called to determine the unit at a specified location in an array. ALBEDO is called to process differential albedo boundary conditions. The library routine GTISO is used to provide direction cosines from an isotropic distribution. _ SFLRA provides a ran-dom number between -1.0 and 1.0 for use in processing anisotropic scattering. SQRT is used in calculating the direction cosines of a history after it has a collision. AZIRN pro-vides the sine and cosine of a random azimuthal angle for use in the anisotropic scattering treatment of a collision.

ALBIN - This subroutine contains the entry point ALBEDO. An initialization call is made to ALBIN by TRACK.

LDWRT- This subroutine prints debug information that is useful only for a programmer. It is called if BUG =YES is specified in the parameter data (see Sect. Fil.4.3). In normal operation, this subroutine should never be called.

MOVE - This library routine is utilized frequently in TRACK _to move data in and out of storage arrays and commons.

TRKWRT - This subroutine is called from various locations in TRACK to print information about the current neutron as it is being processed. RNDOUT is called from TRKWRT to make the current random number available for printing.

FLTRN - This library routine provides a random number between zero and 1. TRACK utilizes these random numbers for playing Russian roulette, processing downscatters, picking fis-

. sion points, determining scattering angles and determining the fission energy group.

CROS- This important subroutine is responsible for processing both inward and outward crossings (i.e., it determines when a history has moved out of one geometry region into another). It determines if a crossing has actually occurred, and if it has, the coordinates of the cross-ing are upgraded to give the crossing point. The fraction of the path length used is also determined.

t Fi l.3.48 l

CROS consists of 'eight major sections. Four geometrical packages exist; one cach for cuboids, cylinders, spheres and hemispheres.11emicylinders are special adaptations of the -

cylinder package. Each geometrical package contains programming for inward crossings and for outward crossings. The variable N indicates the type of crossing being procened; N < 0 checks for an inward crossing and N > O checks for an outward crossing.

The variable M is the crossing indicator, indicating whether or not a real crossing occurs.

M-0 means a real crossing does not occur. M-1 indicates a successful crossing. SQRT is the only library routine utilized in CROS. It is used in the cylinder and sphere pack-ages to solve the quadratic equation for the fraction of the path length that is used.

LOCBOX- This function returns the unit or box type for a specified position in an array.

ALBEDO - ALBEDO is an entry point in subroutine ALBIN. It is responsible for processing a dif-ferential albedo reflection. The direction cosines for the face where the albedo reflection occurs are loaded, and the incident angle and the albedo energy group corresponding to the incident energy group are determined. The position of the albedo energy group within the supergroup, and the first cross-section energy group and the number of cross-section energy groups corresponding to it are determined. This is used to calculate the new cross section energy group of the history. Then the returning angle and direction cosines -

are calculated. The history's weight is then corrected. for the weight lost in the albedo portion of the problem. The weight lost in the albedo reflection is summed.

FLTRN - This library routine is called from ALBEDO to return a random number between zero and one that is used to select (1) the albedo energy group corresponding to the input' energy group, (2) the returning albedo energy group, (3) the returning energy group corresponding to the returning albedo energy group and (4) the returning angle.

EXPRN - This library routine is called from TRACK to provide the number of mean free paths to the next collision. This random number is picked from an exponential distribution.

GTISO - This library routine is called from TRACK to provide direction cosines from an isotropic distribution. These direction cosines are utilized in processing isotropic scattering.

SFLR A - This library routine is called frora TRACK to provide a random number between 1.0 and 1.0 for use in processing anisotropic scattering.

SQRT- This library routine is utilized by TRACK to calculate the direction cosines of a history that has experienced a collision.

AZlRN - This library routine is called from ALBEDO to return the sine and cosine of a random azimuthal angle which are used in determining the direction cosines of the returning history.

1 The remainder of this section is devoted to the logical flow of subroutine TRACK as illustrated by -

Fig. Fil.3.27. The portions of TRACK performing specialized functions are denoted in the text by a j desenptive name enclosed in quotes to distinguish them from subroutine names. These descriptive -

names correspond to the functions depicted in the flow chart. .

1 l

Fil.3A9 ca ,.i o.; m wn

_ \s s'w

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or a usa

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~ ur w uu r m , et

• us t g w., se uwon m .w *

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w

%IilI @"e ., s q{ y= T W]44 m.a s Ntu n os o c ,

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tvtas avt0 7 no a aoa

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( s'v M u ) i

~iurnos artuaws to aaaar i Fig. F11.3.32. Logic flow chart for subroutine TRACK A brief discussion of the logical program flow through subroutine TRACK follows. If differential albedos are used, an initialization call is made to ALBIN. If debug print was. specified in the parameter data, LDWRT is called. The library routine MOVE is used to load data from the neutron bank into COMMON /NUTRON/ and various flags are set. Then the fission source portion of TRACK, denoted *FSTART," initializes and sets information necessary for processing the history. The "PATil* portion of TRACK sets the path length and the end point of the path. The "INWARD* por- .

tion of TRACK determines if an inward crossing is possible and, if it occurs, the point of the boundary crossing. If the history is entering an array from an external region, the 'FINBOX* portion of the code.

determines the history's position relative to the origin of the unit it is entering. If an inward crossing was not possible or did not occur, the " POSIT

• portion of TRACK determines if the end point of the path is in the same . region. If it is, a collision occurs and is processed in the portion of TR.ACK denoted as "XSEC.* Based on the weight of the history, it is split and banked and/or Russian roulette is played. If the history survives Russian roulette,it is scattered and fission points may be generated in the FISSION portion of TRACK, and if it now falls in a different supergroup, it is banked. Otherwise it is retained in the system and processing returns to 'PATii."

Fi 1.3.50 If ' POSIT

• determines that the end point of the path is in a different region, the ' OUTWARD

• por-tion of TRACK processes an outward crossing. If the history remains within the same unit, processing returns to "PATil* to continue as before.

If, after an outward crossing, the new region indicates that the history has crossed out of the unit it was in, the ' ARRAY' portion of TRACK determines if the history is exiting from the artcy or entering a new path. If the history enters a new unit, processing returns to " PATH' and continues as before.

If the history is existing from the array, it can (1) enter the reflector, in which case processing returns to "PATil," (2) leak from the system, thus terminating that history or (3) undergo albedo reflection. The 'AL.BEDO' portion of TRACK can process a specular or mirror image tcDection, a periodic renection, or a differential albedo. For a mirror image or specular reflection, the history is returned at the point it esited with the weight and energy unchanged. The sign of the direction cosine perpendicular to the reflecting face is reversed. For a periodic reDection, the history is moved to the opposing face of the system and the weight, energy and direction cosines remain unchanged. For a dif-ferential albedo reflection the history returns at the point it exited, and subroutine ALBEDO deter-mines the returning weight, energy and angle. The history is then returned to the PATil portion of TRACK to continue processing.

"FSTART* - This portion of TRACK calls the library routine MOVE to load information pertain-ing to the history to be tracked. Then logical Dags are set to indicate if the history is in an array and whether or not the history is a split neutron. Variables are initialized and if the history tracks are to be printed, TRKWRT is called to print information about the history. If the history is the result of an albedo reflection that resulted in the history moving to a new supergroup, and the weight 8s large enough, the history proceeds to the ' PATH" portion of TRACK. Otherwise Russian roulette is played.

If it survives, the weight is set to the ayerage weight and the history proceeds to the

' PATH' portion of TRACK. If the history is a split neutron, variables are initialized and the history proceeds to the "XSEC' portion of TRACK to undergo the collision process.

-PATH"- This portion of TRACK determines the path length, if all the path length has been exhausted, the library routine EXPRN is used to define a new number of mean free paths from an exponential distribution. If the region contains a void, the distance traveled is set to the maximum chord length of the system. Otherwise the distance traveled is equal to the remaining path length, divided by the macroscopic total cross section of the mixture contained in the region. The end point of the path is deter-mined from the starting coordinates, the distance traveled and the direction cosines, if the starting and ending coordinates are identical in any given direction, the end i point is changed by a very small amount in the proper direction.

l

! *INWARD* - This portion of TRACK decides whether or not an inward boundary crossing is possi-ble, and if it is, calls CROS to determine if a crossing actually occurs and the coordi-nates of the crossing. Each time CROS is called, the library routine MOVE is used l to load the geometry region dimensions of the possible new region into COMMON /

l NUTRON/ to be used by subroutine CROS. The crossing indicator is set to l instruct CROS to check for an inward crossing and the possible new region type is set. If the history tracks are to be printed, TRKWRT is called to print information pertinent to the crossing. Subroutine CROS sets a crossing indicator that informs TRACK whether a crossing occurs as well as determining the coordinates of the crossing. If a crossing occurs, the appropriate contributions are summed into the flux and neutron age. Then the number of mean free paths remaining for the history is determined.

i F11.3.51 When checking for an inward crossing, a check is made to determine if the history is in the innermost region of a unit and whether the innermost region contains holes.

An inward crossing is not possible if the history is in the innermost region and that region does not contain holes. If holes are present in the innermost region, each hole in the region must be checked for a crossing.

If the history is not in the innermost region, an inward crossing is possible if holes are present, egen if the last crossing was outward. CROS determines if an inward -

crossing actually occurs. If a crossing does not occur and no holes are in that region, tracking proceeds to the TOSIT* portion of TRACK. If a crossing did occur and holes are not present in that region, the flux and neutron age are updated and track-ing proceeds to the TINBOX* portion of TRACK. Tracking proceeds to the TOSIT* portion of TRACK if an inward crossing is not possible and no holes are in the region.

If holes are present in the region, after checking for an inward crossing, each of the holes is checked for an inward crossing. This involves transforming the coordinates of the history to the coordinate system of the hole and calling CROS to determine if the history crosses into the outer region of the hole, After repeating this procedure for each hole in the region, the crossing with the shortest distance is selected as the actual crossing. If the crossing is into a hole, the coordinates of the history are transformed to the coordinate system of the hole and tracking proceeds to the TIN.

BOX" portion of TRACK. The correct new region number is set whenever an inward crossing occurs.

-FI N BOX" - This portion of subroutine TRACK is responsible for determining when a history enters a new array and for performing the transformation of coordinates whenever a history travels from a surrounding region into an array, it alsa determines the loca-tion within the unit orientation array of the unit containing the history. This infor-mation is used to determine the unit type, and the first and last regions of the unit.

-POSIT * - This portion of TRACK determines if the path ends in the same region in which it originated.

-OUTWARD

• An outward crossing occurs when the TOSIT* portion of TRACK determines-that the nistory is entering a different region. The library routine MOVE loacts the dimensions of the new geometry region into COMMON /NUTRON/ for use by subroutine CROS. The crossing-type indicator is then set to instruct CROS to pro-cess an outward crossing. If history tracks are to be printed, TRKWRT is called to print information pertinent to the outward crossing. CROS determines the coordi-nates of the boundary crossing. The contribution of the history is summed into the flux and neutron age and the number of mean free paths remaining for the history is calculated. The region number is incremented. If the old region was not the last region in the unit, a logical flag is set to avoid some of the checking for an inward crossing for the next boundary crossing. Tracking then proceeds to the TATil' por-f tion of TRACK. The region number is set to the last region in the unit, if the old region was the last region in the unit. If the problem is a single unit problem or the history is exiting the external reflector, the history proceeds to the ' ALBEDO

• por-tion of TRACK to leak from the system or process an albedo reflection. If the his-tory has exited a unit in an array, tracking proceeds to the " ARRAY" portion of TRACK to continue the tracking process.

Fi l.3.52

" COLLISION" . When a history has a collision, the processing is done in this portion of TRACK. If fluxes are to be calculated, the new contribution is summed in. The age of the his-tory is summed, the remaining path length is set to zero, the absorption weight, fis-sion weight and the contribution to the average number o.* neutrons produced per fis-sion and the self multiplication of the unit are calculated, based on the macroscopic cross-section data and the weight of the history. The weight of the history is then redefined to be the weight times the macroscopic nonabsorption probability. If the history tracks are to be printed, TRKWRT is called to print information pertinent to the collision process. If matrix k-effectives are to be calculated, the fission weight is summed into the proper arrays. If the weight of the history exceeds the weight at which splitting occurs, a check is made to assure the neutron bank has adequate space for another history. If it is full, a message is written and Russian roulette is played. If the bank can hold another history, the weight of the history is halved and the neutron counter is incremented. If the history tracks are to be printed, TRKWRT is called to print information pertinent to the split neutron. The library routine MOVE is used to store the split neutron in the neutron bank. The history cycles through the checking and splitting process until its weight is less than the weight at which splitting occurs. Then the weight is checked to see if Russian rou-lette should be played if it is played and the history survives, the weight is set to the average weight. If Russian roulette is not played, the weight remains unchanged. In both cases, the new energy group is computed and a check is made to determine if the history undergoes anisotropic scattering. If it does, the azimuthal angle is chosen using AZIRN and the sine and cosine of that angle are returned to be used for cal-culating new direction cosines. If the history does not undergo anisotropic scattering, the new direction cosines are chosen from an isotropic distribution using _GTISO.

This completes the ' COLLISION" portion of TRACK.

" FISSION" - This portion of TRACK is responsible for generating and storing the fission source resulting from a collision. In the ' COLLISION

• portion of TRACK, the fission weifht is defined as the weight of a history times the macroscopic production proba-bility, If the fission weight of a history is greater than zero, the ' FISSION' portion of TRACK is executed. To assure generating enough fission source points to main-tain an adequate representation of the true distribution, a minimum production factor is defined at the beginning of each generation to be 3.0F di5 where f is the running average value of the k-effective through the current genera-tion and FG is the number of histories per generation. This represents an estimate of the lower limit of the 99% confidence interval for the distribution of the generation k-effective. Experience indicates that using this factor to generate fission source points leads to enough new fission points to fill the neutron bank for most generations.

When the ' FISSION

• portion of TRACK is entered, the library routine FLTRN is used to provide a random number that is saved. A pseudo fission weight is defined as the fission weight divided by the random number. If the result is less than the production factor, the history proceeds to " PATH" or is stored in the neutron bank,

F11.3.53 depending on whether or not it remains in the same supergroup. If the his'ory t .

remained in the ' FISSION

• section, and its fission weight is greater than the production factor, the pseudo fission weight is redefined to be the production factor divided by the random number. If the fission bank is not full, the fission energy group is determined using FLTRN, the fission point is stored in the bank, and the number of fission points is incremented. The library routine MOVE is used to load information pertaining to the fission point from COMMON /NUTRON/ into the fission bank and the pseudo fission weight is loaded directly into the fission bank. If the fission bank is full when a new fission source point is generated, the bank is searched for the smallest pseudo fission weight. This is compared with the pseudo fission weight of the new fission point and the point having the larger pseudo fission weight is stored in the bank. After the fission point has been banked, the fission weight of the history is decremented by the production factor. If the remaining fis-sion weight is greater than rero, the history returns to the beginning of " FISSION

• to continue processing.

-ARR AY* - This portion of TRACK is responsible for processing a history that crosses a unit or box type boundary, This occurs only when the history is moving in an outward direc-tion.

A check is made to determine if the history is exiting from a unit in an array or a umt used as a hole; if the exited unit was used as a hole, the coordinates are transformed to the coordinate system of the region containing the hole. The history then proceeds to the "PATil* portion of TRACK. Ilowever, if the unit exited by the history was part of an array, a check is made to see if tracks are to be printed. If so, TRKWRT is called to print pertinent information about the history. Each face of the unit is checked in sequence to force proper positioning for face, edge and corner crossings. As each face is processed, the position of the unit witt.in the unit orienta-tion array is updated as appropriate (this is done by incrementing the X, Y and/or Z indices of the unit position). A logical flag is set for each t' ace to indicate if the his-tory is exiting from the array, After all faces have been processed or bypassed, a check is made to determine if the history remains within the array, if it does, the -

new unit type is determined from the position indices of the location witbin the unit orientation array, and a transformation of coordinates is done to correct for crossing into the new unit. If the new unit consists of only one region, the history proceeds to

'FINBOX' to determine if the history is entering a new array. The history then pro.

ceeds to "PATil' to continue processing. If the history exitea the global array, a check is made to determine if a ref%: tor is external to it. If not, the history leaks from the system or proceeds throur,i the *ALUEDO' portion of TRACK as appropri-ate. If surrounding geometry exists where the history exits an array, a transforma-tion of coordinates provides the history's position relative to the surrounding geome-try. The history then proceeds to the *PATil" portion of TRACK and tracking continues.

-ALBEDO'- If an albedo boundary condition is specified on any face of the problem, this portion of TRACK is utilized to provide the proper treatment. Each face is checked in sequence to determine if the history (1) leaks from the system, (2) undergoes specu.

lar or mirror image reflection, (3) undergoes periodic reflection, or (4) proceeds through the differential albedo treatment.

If the history undergoes specular or mirror image reflection, it is returned at the point it exited the face with its energy unchanged and the sign of its direction cosines reversed. If a periodic reflection occurs, the history is moved to the opposing face with its energy and direction cosines unchanged. If the history enters a differential

Fil.3.54 albedo renector, subroutine ALBEDO is called to determine the new weight of th history and its returning angle and energy. If the history enters a new supergroup, TRKWRT may be called to print the history track infortnation and MOVE is called to bank the history in the neutron banL When a history remains in the same super-group, it is returned at the point it exited and Russian roulette is played if the returning weight is low enough to warrant that action. If the weight in sufficiently high to avoid playing Russian roulette or if the history sur'ives Russian roulette, the history proceeds to the beginning of 'PATil' and tracking continues.

F l l .3. l 3.. Provide the Next cirneration Source O n N L -- DWG 8019219 R I

NSTART n m ~

r SORTBK r o m y b $c 5 E o O H 5 5 Fig. Fil.3.33. Flow chart for providing the next generation soutec This section of the program is responsible for providing the source for the next generation from the fission source generated during the tracking procedure.

NSTART- This subroutine calls CLEAR to initialize the neutron bank and writes an error men. ,e if no fission points were generated. Subroutine SORTBK is called to move information from the fission bank containing the fission source generated by the last generation into the neutron bank to be used as the source for the next gerieration. NSTART then checks to be sure enough source points exist to start the next generation. If too few starting points exist, the library routines MOVE and FLTRN are used to fill the required number of starting positions from the existing fission points.

SORTBK - This subroutine sorts the fission bank so the fission points are loaded in the order of their probability of being picked in a random selection process. For each source history, the library routine MOVE is used to move the fission source generated by the last generation into the neutron bank, and the library routine GTISO is used to provide direction cosines from an isotropic distribution. Then the neutron number, weight and age are initialized.

Fil.3.55 l

Fil 3.13.5 End of Generation Processing ORNL-DWG 8019220R FISFLX l l MATK LOOPE R E m

I i (n o o r-m x i I H > m m m 4 o STATIS m Fig. Fil.3.34. Flow chart for end of generation processing This portion of the program is responsible for processing data at the end of each generation.

FISFLX - This subroutine is called at the end of each generation to process data collected for that generation. The generation k effective, the running average value of k effective and its '

deviation, and the tantrix k effective and its deviation are processed and printed. MATK is called to process the matrix k effective (s) and associated information. LOOPER is called and, in turn, calls STATIS to collect and process the contribution and statistics for the flux, fissions, and absorptions, as well as the contribution to the leakage.

MATK- This subroutine is called to calculate the matrix k effective by solving for the principal eigenvalue end eigenvector of a matrix using an iterative technique. The library routine CLEAR is used to initialize arrays and SQRT is used in calculating the deviation of the eigenvalue. MATK may be called to calculate the rnatrix k effective by array positi>n, .

unit type, array number, and/or hole number, i

LOOPER- This subroutine is called from FISFLX to load arrays in preparation for calling STATIS.

A loop is made over the number of supergroups, within which pointers are calculated, REED is called to load the leakage,6bsorption, fission and flux arrays from the direct access supergroup file, STATIS is called to process the data and RITE writes the pro-cessed data on the direct access supergroup file. This procedure is repeated until all supergroups have been processed.

[

Fi l.3.56 STATIS - This subroutine collects the sum of the contributions and the sum of the square of the contributions for the fluxes, fissions, absorptions and leakages to be used at the end of the problem in calculating their deviations.

Fil.3.14 END OF PRO 11LEM PROCESSING ORN L-DWG BO 19216R2 KE DIT I

fl l I l 5

l l

$0 mo PLTKEF LOOPE R e

o M AT RIX HT C o H

llll m c I I- I H l l I coog l EC$O zy2H 0 $

m MATK

$55 m tu d m r- g o H m

n i EDITOR gp i

x a > m o 2 o

E Fig. Fil.3.35. Flow chart for end of problem processing This portion of the program is responsible for processing data and printing all the results except the fluxes at the completion or terminat:on of a problem.

KEDIT - This sub outine controls the processing and priging of results at the end of a problem.

The life time and generation time are printed and,if the average number of neutrons per fission was calculated, it and the average fission group are printed. KEDIT then calcu-lates and prints the average k effective and its associated deviation for the 67,95, and 99% confidence intervals and the number of histories involved. This is done repeatedly, skipping more generations each time. PLTKEF is called to print a plot of the average ,

value of k-effective as a function of the number of generations, it also pr nts a plot of the i

average value of k effective as a function of the number of generations skipped.

LOOPER is called to prepare data for EDITOR which in turn calculates and prints the groep-dependent fissions, absorptions and leakages and their deviatieas, if requested, the fissions and absorptions may also be printed by region. KEDIT then prints the total fisi ,

sions, absorptions and leakages for the system, and their associated deviations. RNDOUT is called to provide the current random number to be printed. If matrix k-effective data .

were requested. MATRIX is called to calculate and print matri.t infor nation. KEDIT then processes and prints the fission densities.

Fl 1.3.$7 l

, l PLTKEF- This subroutine is called from KEDIT to print a plot of the average value of k effective I versus generation and a plot of the average value of k effective versus generations skipped, )

The library routines DMINI, DMAXI, and DSQRT are used to generate the k-effective axis of the plots. The MOD function is used in labeling the generation axis.

LOOPER - This subroutine is called from KEDIT to load arrays in preparation for calling EDITOR.

A loop is made over the number of supergroups. Within the loop, pointers are calculated.

REED is called to load 11: leakage, absorption, fission and flus arrays from the direct access supergroup file and EDITOR is called to process the data. RITE then writes the processed data for the supergroup on the direct access supergroup file.

EDITOR - This subroutine is called from LOOPER to calculate and print the energy dependent fis-sions, absorptions and leakages and their deviations. The fissions and absorptions may be region dependent as well as energy dependent.

M ATRIX - This subroutine is called from KEDIT to calculate and print various information related to the matrix k-effective, it is called if one or more matrix options were specified in the parameter data (see Sect. Fil.4.3).. If matrix information was collected, MATK is ,

called to calculate cofactor k.cffectives. MATRIX then prints them as they are calcu-lated. MATRIX also prints the fission production matrix if that was specified in the parameter data (see Sect. Fil.4.3). The library routine LAllt is called to print the source vector. MATRIX then prints the average self multiplication calculated on the basis of collected data. This procedure is repeated for each type of rnatrix information specified in the parameter data. JSTIME is called to determine the amount of time used in the problem, which is then printed in MATRIX. ,

MATK- This subroutine calculates the principal eigenvalue and eigenvector of a matrix using an iterative technique. It also calculates the deviation associated with the eigenvalue, using CLEAR to initialize arrays and SQRT in calculating the deviation. MATK may be called from MATRIX to calculate cofactor k-effectives.

Fil.3.15 l'RINT FLUXES O ftN L-DWG 80 19217 FITFLX l.

x I o-pRTFLX l '

v>

l O x

! -4 Fig. Fil.3.36, Flow chart for printing fluxes

_- < , < - - -e e ,,,,,-n,.- ~nc-.-- + - , - - - - --,w --.4 , - , , - - - - r e-- -, w- -r-.-y---w,,,,, - w - , - +-r,u

._ _ _ _ _ . . _ . . _ . _ . _ . _ . _ = - _ _ _ _ _ _ . _ _ . _ . _ _ _ _ _ _ _ . _ _ _ . _ _ . _ . _ _ _ _ _

Fil.3.38  !

l This portion of the prograin is responsible for printing the fluxes at the completion of a problem.

FITFLX - This subroutine determines the maximum number of regions for which nun data will fit in memory and loads and prints them as they will fit. Pointers are calculated and the hbrary routine RD is used to load the fluxes for those regions from the direct access supergroup file. PRTFLX is called to calculate the deviations and print the region. and  !

~

energy-dependent Dutes and their associated deviations. If more Outes remain to be printed, the process is repeated until all have been printed.

PRTFLX - This subroutine normalites the Huxes, calculates their deviations and prints them, one supergroup at a time. The library routine SQRT is used when calculating the deviations.

Fil.3.16 REFERENCES I. S. K. Fraley, Users Guide for /CE //, ORNL/CSD/TM-9/R1 (July 1977). Also see Sect. F8 -

of the SCALE manual.

2. ' Appendix U, Generalized Gaussian Quadrature,* The Aforse Code A hfultigroup Neutron and-Gamma Ray hionte Carlo Transport Code GRNL-4585 (1970). -Also see Sect. F9.DJ of the SCALE manual.

y

Fil.4 KENO Y DATA GUIDE KENO Y may be run

• stand alone* or as a part of a SCALE criticality safety sequence. If '

KENO V is run

• stand alone,' cross section data can be utilized from an AMPX' working format  ;

library or from an ICE (Sect. F8) rnised cross-section MORSE / KENO format library, also called a Monte Carlo formatted cross section library, if KENO V uses an AMPX working format library, a  ;

mixing table data block must be entered. If an ICE mixed cross-section MORSE / KENO library is used, a mixing table data block is not entered and the mixtures specified in the KENO V geometry description must be consistent with the mixtures created in ICE. These are the entries in the ll5[ MUD] array in the ICE input data.

If KENO V is run as part of a SCALE criticality safety sequence, the mixtures are defined in the CSAS4 data (Sect. C4.4) and a mixing table data block cannot be entered in KENO V. Further.

more, the mixture numbers used in the KENO V geometry description must correspcmd to those defined in the standard composition cards of the CSAS input. A mixture number of 500 miat be used nr. the KENO V geometry description in order to use a cell weighted mixture. A cell weighted mix-ture is available only in SCALE sequences that do a cell weighting calculation, r11.4.1 KENO V INPUT GUTLINE The data input for KENO V is outlined below. Defaulted data for KENO V have been found to be adequate for many problems. These values should be carefully considered when entering data. The information in llOLD TYPE is entered as data.

tilocks of input data are entered in the form: 1 READ XXXX input data END XXXX where XXXX is the keyword for the type of data being entered. The keywords that can be used are listed in Table Fil.4.1. . A minimum of four characters are required for a keyword, llowever, the key-words can be up to twelve characters long, the first four of which must be input exactly as listed in the table. Data input is activated by entering the words READ XXXX followed by one or more blanks. All  ;

input data pertinent to XXXX are then entered. Data for XXXX are terminated by entering END XXXX followed by two or more blanks.

Table Fil.4.1. Types of input data Type of Data First 4 Characters parameters PARA or PARM geometry OEOM biasing BIAS -

boundary conditions BOUN or DNDS start STAR or STRT array (unit orientation) ARRA extra 1 D cross sections X1DS cross section Mixing Table

• MIXT or MIX plot or picture

• PLOT or PLT or PICT

• MIX and PLT must include a trailing blank which is considered part of the keyword.

I Fi l .4.1

1 Fi l .4.2 l

"There stre two data cards that must be entered for every problem. The first is the problem title.

The second is the END DATA to terminate the problem.

(1) prottlem title J Enter a problem title (limit, one card, i c., 80 characters including blanks). A l title must be entered. j See Sect. Fil.4.3.

(2) READ PARA parameter data END PARA i l

Enter parameter irout as needed to describe a problem. Default values are assigned to all parameters. A problem can be run without enterinF any parame-ter data if the default values are acceptable.

Parameter data must begin with the words READ PARA. Parameter data may l be entered in any order. If multiple entries are made for a pararneter, the last value is used. The words END PARA terrninate the parameter data.

See Sect. Fil.4.3. )

l (3)...(9) The following data may be entered in any order. Data not needed to describe the problem may be omitted.

(ni) READ GEOh1 all geometry region data END GE051 Geometry region data must be entered for every problem that is not a restart problem. Geometry data must begin with the words READ GEOS1. The words

. END GEON1 terminate the geometry region data.

See Sect. Fil.4.4.

(n2) READ ARRA array definition data END ARRA 1

Enter array definition data as needed to describe the problem. Array definition l data define the array size and position units (defined in the geometry data)in a three-dimensional lattice that represents the physical problem being analyzed.

Array data must begin with the words READ ARRA. The words END ARRA terminate the array data.

See Sect. Fil.4.5.

(n3) READ DIAS blasing information END BIAS liiasing information is used to derme the weight that is given a neutron surviving Russian roulette. Enter biasing information as needed to describe the problem.

Biasing data must begin with the words READ BIAS. The words END BIAS ter-minate the biasing data.

Sec Sect. Fil.4.7.

(n4) READ BOUN albedo boundary conditions END BOUN Enter albedo boundary conditions as needed to describe the problem. Albedo data must begin with the words READ BOUN and terminate with the words END HOUN.

See Sect. Fil.4.6.

Fi 1.4.3 (n s) READ STAR starting distribution information END STAR Enter starting information data for starting the initial source neutrons only if a uniform starting distribution is undesirable. Start data must begin with the words READ STAR and terminate with the words END STAR.

See Sect. Fil.4.8.

I (n6) READ MIXT cross section mixing table END MIXT Enter a mixing table to define all ihe mi.v.tures to be used in the rcoblem. The mixing table must begin with the words READ MIXT and end with the words END MIXT. Do not enter mixing table data if KENO Y is run as a part of a  !

SCALE criticality safety sequence.

See Sect. Fil.4.10.

(n7) READ XIDS extra I.D crowsection ID's END XIDS I

Enter the ID's of any extra one dimensional cross sections that are to be used in the problem. These must be available on the mixture cross section library. Extra 1 D cross-section data must begin with the words READ X1DS and terminate with the words END XIDS.

See Sect. Fil.4.9. ,

(ns ) ItEAD PLOT plot data END PLOT Enter the data needed to provide a two-dimensional printer plot of a slice through a specified portion of the three dimensional geometrical representation of the problem. Plot or picture data must begin with the words READ PLOT and terminate with the words END PLOT.

See Sect. Fil.4.ll.

(n.) END DATA must be entered Terminate the data for the problem.

Fi l.4.2 PROCEDURE FOR DATA INPUT This section is a brief list of the input data for KENO V. Additional information concerning KENO V data input may be found in Sect. Fil,5. The first card of data must be the title. The next block of data must be the parameters if they are to be entered. A problem ca.n be run without entering the parameters. The remaining blocks of data can be entered in any order.

Il0LD TYPE specifies keywords. A keyword is used to identify the data that follow it. When a keyword is used, it must be entered exactly as shown in the data guide. All keywords, except those ending with an equal sign, must be followed by at least one blank, small italics correlate data with a program variable name. The actual values are entered in place of the program variable name and are terminated by a blank or a comma.

Fil A.4 CAPITAL ITAL /CS identify general data items. General data items are general classes of d[ta including i

\\) geometry data such as UNIT INITIALIZATION and UNIT NUAfBER DEFINITION, GE0AfETRl' REGION DESCRIPTION, GEOAfETRl' If*0RD Atla 7URE NUAfBER, BIAS ID and REGION DIAIENSIONS, L

t (2) albedo data such as FACE CODES and ALBEDO NAAfES, (3) weighting data such as BIAS /D NUAIBERS, etc.

Fil A.3 TITLE AND PARAMETER DATA TITLE . . A title must be entered.

f tit /c one card,80 characters including blanks PARAMETER DATA . . . Enter only those whose values you wish to change. The commonly changed ,

parameters are TAfE. GEN, and NPG. Seldom changed parameters are NBK, NFB, LBK, LFB, WTH,

-ISTL. TBA. BUG, TRK, and LNG.

READ PARAM Floating point parameters RND - rndnum input hexadecimal random number, a default value is provided.

TME=tmax execution time (in minutes) for the problem, defauit - 30 minutes.

TBA - tbtch time allotted for each generation (in minutes), default = 0.5 minutes.

If tbtch is exceeded in any generation, the problem is terminated and final edits are perfon 'd. ,

WTA - dwtav the default average weight given a neutron that survives Russian roulette, ,

dwtav default - 0.5.

WTil - wthigh the default value of wthigh is 3.0 and should be changed only if the user has a valid reason to do so. The weight at which splitting occurs is defined to be wthigh x wtavg. where wtavg is the weight given to a neu.

tron that survives Russian roulette.

WTL - wtlow Russian roulette is played when the weight of a neutron is less than witow x wtavg. The wilow default = l.0lwthigh.

NOTE:The default values of wthigh and wtlow have been determined to minimize the deviation per unit running time for many problems.

~- .

. - - - -. . - - - - ~ . ._. . . -_. - --- - - _ _

l i

Fi l.4.5 4

Integer parameters CEN = nba number of Fenerations to be run, default - 103 NI'G - npb number of neutrons per generation, default - 300 NSK - nsA 'p number of generations (1 through nskip) to be omitted when collecting results, default - 3 RES - nrstri number of generations between writing restart data, default - 0.

If RES is zero, restart data are not written. When restarting a problem.

R13 is defaulted to the value that was used when the restart data bkick ,

was written. Thus, it must be entered as zero to terminate writing restart data for a restarted problem. (WRS is the logical unit number for writing restart data. See logical unit numbers in the parameter data.)

N!!K - nbanA number of positions in the neutron bank, default - npb + 25 XNil - ntnbA number of extra entries in the neutron bank, default - 0 NFil - it/bnA number of positions in the fission bank, default - npb XFil - nxfb4 number of extra entries in the fission bank, default -0 XID - numxid number of extra 1 D cross sections, default - 0 LNG - Ing number of words of storage to be requested by subroutine ALOuT, default - 4000000 (This is reduced to fit in the space allotted to the job when the problem is run.)

110G - nbas beginning generation number, default - 1 If REG is greater than 1, restart data must be available.

Nil 8 - nb8 - number of blocks allocated for the first direct access unit, default - 200 NIJl - n/3 length of blocks allocated for the first : direct access unit, default - 789 Alphanumeric parameter data , , , enter YES or NO RUN - frun key 'for determining if problem is to be executed when data checking is -

complete, default - TES Note: The value of RUN set here will be overridden by a value entered in the PLOT data, llowever, if the problem is restarted, the default value or the value entered here is the value that will be used unless the PLOT data block from the restart unit is overridden by new PLOT data. See Sect. Fil.4.9.

+1 gr v'sei-wrq--

- -,,n- 4% e ,#e -

---

m- -w- y ,45-y -g g wg. g y gw-, yem 's g y- -- ,< rv --

. -. . _ . - _ . - - . - - - _ .-. .- . ._- . . -- .. = . _ - -

Fila 6 FLX - nJ71 Ley for collecting and printing flutes, default - NO FDN - nfden key for collecting and printing fission decsities, default - NO ADJ - nadj key for running adjoint calculation, default - NO. Adjoint cross sections must be available to run an adjoint problem. If Lill- is specified, the cross sections will be adjointed by the code. If XSC=

is specified, the cross sections must already be in adjoint order.

AMX-amt key for printing all mixture cross section data. This is the same as activating XAP. XSt. XS2. PK/, and P/D. If any of these are  ;

entered in addition to AAfX, that portion of AAIX will be overridden, default - NO, XAP prrup key for printing discrete scattering anF les and probabilities for the mixture cross sections, default - NO XS1 perp0 Ley for printing mixture I D cross sections, default - NO XS2 pril key for printing mixture two-dimensional cross sections, default - NO PKI perchi print input fission spectrum, default - NO PID prrex print extra l D cross sections, default - NO FAR - Ifa key for printing fissions and absorptions by region, default - NO M EP - tarpos calculate and print matrix k-effective by unit location, default - NO. Unit location may also be referred to as array position or position index.

CKP -IcAp calculate and print cofactor k effective by unit location, default is the value of AIKP. Unit location may also be referred to as array posi-tion or position index.

FMP pmapos print fission production matrix by array position, default - NO i MKU = /unft calculate and print matrix k effective by unit type, default - NO CKU - IcAu calculate and print cofactor k-effective by unit type, default is the value of AfKU 1310 pmunit print fission production matrix by unit type, default - NO MKil - Imhole calculate and print matrix k effective by hole number, default - NO 1

F i 1.4.7 CKil = IcAh calculate and print cofactor k-effective by hole number, default is the value of MKit.

I Mil = pmhole print fission production matrix by hole number, default = NO lillt = lhhgh collect matrix information by hole number at the highest hole nesting level, default - NO MK A = frwry calculate and print matrix k-effective by array number, default - NO CKA - IcAa calculate and print cofactc.r k effective by array number, default is -

the value of MKA I MA = pmarry print fission production matrix by array number, default - NO II AL = langh collect matrix information by array number at the highest array nest-ing level, default - NO PLT - Irlot key for drawing specified pictures of the problem geometry, default -

YES Note: To draw a plot, appropriate plot data must be entered. The value of PLT set here will be overridden by a value entered in the PLOT data. liowever, if the problem is restarted, the default value or the value entered here is the value that will be used unless the PLOT data block from the restart unit is overridden by new PLOT data. See Sect. F i l .4.9. The value of Iplot set here is written on the restart unit and the value of Iplot set in the PLOT data is not.

HUG = idbug print debug information, default = NO Enter PES for code debug purposes only.

TRK = ltrA print tracing information, default = NO Enter YES for code debug purposes only.

PWT=Ipwt print weight average array, default = NO PGM = Igcom print unprocessed geometry as it is read, default = NO SMU = /mult calculate the average self-multiplication of a unit, default = NO NUB = newbar calculate the average number of neutrons per fission and the average energy group at which fission occurred, default = NO PAX = Icorsp print the arrays defining the correspondence between the cross.

section energy group structure and the albedo energy group struc-ture, default = NO

Fi l.4.8 Logical Unit Numbers XSC - xirrs logical unit number for mixed cross sections, default = 14 Al.it - albdo logical unit number for albedo data, default = 79 W 1 S = wts logical unit number for weiF hts, default = 80 1.111 = lib logical unit number for AMPX working library, default =0 SKT - 5 Art logical unit number for scratch space, default - 16 RST - rstri logical unit number for reading restart data, default =0 Enter a logical unit number to intatt with BEG = 1 WRS = wstra logical unit number for writing restart data, default = 0 A non zero value must be entered if RES > 0.

Fi l.4.4 GEONIETRY DATA GE0hlETRY REGION DATA . . geometric arrangements in KENO are achieved in a manner similar to using a child's building blocks. Each building block is called a UNIT or BOXTYPE. An array or lattice is constructed by stacking these units or box types. Once an array or lattice has been constructed,it can be placed in a unit by usinF an ARRAY or CORE specification.

Each UNIT in an array or lattice has its own coordinate system; however, all coordinate systems in all units must have the same orientation. All geometry data used in a problem are correlated to the absolute coordinate system by specifying a global unit or a global array. UNITS are constructed of combinations from several allowed shapes or geometric regions; i.e., cubes, rectangular parallelepipeds, cylinders, spheres, hemispheres, and hemicyhnders These regiuns can be placed anywhere within a UNIT as long as they are oriented along the coordinate system of the unit and do not intersect other regions. This means, for example, that a cylinder must have its axis parallel to one of the coordinate axes, while a rectangular parallelepiped must have its faces perpendicular to a coordinate axis. The most stringent KENO geometry restriction is that none of the options allow geometry regions to inter-sect. Figure Fil.4.1 shows some situations that aren't allowed.

ORNL-DWG 83 14790 C h n i r T l u 4 1 z

v INTERSECTING REGIONS INTERSECTING REGIONS ROTATED REGION Fig. FI1.4.1. Examples of geometry not allowed in KENO

F i l .4.9 Unless special options are invoked, ca:h geometric region in a UNIT must completely enclose each

. interior region, llowever, regions can touch at points of tangency and share faces. See Fig. Fil.4.2 for examples of allowable situations.

OHNL-DWG 83-14791 (m)

REGIONS ENCOMPASS-:NG REGIONS ENCOMPASSING INTERIOR REGIONS REGIONS AND TOUCHING Fig. Fil.4.2. Examples of correct KENO units Special options are provided to circumvent the complete enclosure restriction. These fall under the heading EXTENDED GEOMETRY DESCRIPTIONS and include ARRAY and llOLE descriptions.

The llOLE option is the simplest of these and allows placing a unit anywhere within a region, as long as intersections do not occur. See Fig. Fil.4.3.

OHNL-DWG 8314760 l

t I

I

) L UNIT 1 UNIT 2 UNIT 2 WITH UNIT 1 PLACED IN IT AS A HOLE Fig. Fil.4.3. Example demonstrating HOLE capability in KENO An arbitrary number of IlOLES can be placed in a region in combination with a series of surround-ing regions.

Lattices or atrap are created by stacking UNITS that have a rectangular parallelepiped outer region. The adjacent faces of adjacent units stacked in this manner must match exactly. See Sect. Fil.5.6.4 for additional clarification and Fig. Fil.4.4 for a typical example.

l-11.4.10 ORNL-0WG 8314189 UNIT 2 O O O O O e ~ ,, ,

' > O O O O O O O O O CHL ATE UNITS ST ACK THE UNITS TO FORM AN ARRAY Fig. Fil.4.4. Example of array construction The ARRAY option is provided to allow placing an array or lattice within a unit. Only one array can be placed directly in a UNIT, llowever, multiple arrays can be placed within a unit by using IlOLES. When an array is placed in a unit via a HOLE, the unit that contains the array, rather than the array itself, is placed in the unit. Arrays of dissimilar arrays can be created by stacking units that contain arrays. See Fig. Fil.4.5 for an example of an array composed of units containing holes and arrays.

ORN L-DWC ',3 . ,4 787 O O O O n OOOO oo r oo1 OOOO

\ o o) o o o o 00 v ggym OOOO O O O O h-UNIT CONT AINING-* H ARRAY IN H~ ARR AY IN *(- ARR AY IN :l HOLES A UNIT A UNIT A UNIT Fig. Fil.4.5. Example of at trray .omposed of units contain:ng arrays and holes

. - . ~ - . - - . . . . - . - .

Fi l.4.l i The method of entering GEOMETRY REGION DATA follows:

READ GEOM GEOMETRY REGION DATA END GEOM '

GEOMETRY REGION DATA rnust be entered unless the problem is being restarted. A descrip-tion of all units or box types the user wishes to define must be entered. S:e Sect. Fil.5.6 for detailed exarnples. ,

The dentiption of a unit includes all peometry data following a UNIT INITIAllZATION. A unit is terminated by encountering another UNIT INITI ALIZAllON or an END GEOM.

A GLOMETRY REGION DATA description consists of one or more of the following: ,

(a) UNIT INITI ALIZATION (b) SIMPLE GEOMETRY REGION DESCRIPTION * '

(c) EXTENDED GEOMETRY DESCRIPTION  :

(d) OPTIONAL GEOMETRY COMMENTS .

t tal UN/T INITIAI.12ATION . . This data sequence signals the beginning of a new geometric coordinate system and assigns the unit number to the geometry regions comprising the unit.

A UNIT INITIALIZATION is invoked when one or more of the following data items are '

encountered:

(al) OPTIONAL GLOllAL SPECIFIC ATION .i (geom ,

GLOBAL The word GLOBAL, if entered, must be followed by one or more blanks and a UNIT NUMBER DEFINITION and/or an ARRAY PLACEMENT DESCRIPTION. Enter the geometry word GLOBAL immediately prior to the UNIT or ARRAY that defines the over.

all geometric boundaries of the problem. The code defaults the global array to the array referenced by the last ARRAY PLACEMENT DESCRIPTION that is not immediately preceded by a UNIT NUMBER DEFINITION Otherwise, it is the largest array number-specified in the array data (Sect Fil 4.5).

(a2) UNIT NUMBER DEFINITION KEYWORD UNIT NUMBER Igcom nbox

! UNIT. enter unit ID number or BOX TYPE enter unit ID number l or BOXTYPE enter unit ID number The UNIT NUMBER definition assigns the specified unit number to the geometry data that define the unit.

l

,i.,.

.,.-..-,...-..___,_...-_.-...-4.._ _ , - . . - . . . _ _ _ _ - _- J. .a__._-._,_...J,-._..._.- . . . .

i i

Yl l.4.8 2 I

(a3) ARRAY PLACEMENT pt SCRIPTION freom(") -  ;

ARRAY or ,

CORE or COREllDY f Of COREBNDS f or -

COR EllOUN

" Additional data are required as described in the EXTENDED GEOMETRY DESCRIP.

TlON.

The array placement description is used to place a specified array in a UNIT. It positions the most negative point of the array relative to the origin of the UNIT.

(b) SIAfPLE GE0AfETRI' REGION DESCRIPTION ._ . . This type of geometry data consists of -

simple shapes whose specification is independent of other geometry regions. Free form input is '

used to enter the data. Options R. *, 5. and P from Table Fil.4.2 can be used. Each SIM-PLE GEOMETRY REGION DESCRIPTION is entered in the form:

GE0AfETRl' WORD Jgeom AllXTUREID ,

mat BIAS ID imp i APPROPRIATE REGION DIAfENSIONS xx

. 0PTIONAL REGION DATA .

' origin data and/or chord data -

The GE0AIETR)' WORDfgrom is followed by one or more blanks and must be one of the keywords below, CUBE, CUHOID, SPilERE, CYLINDER, ZCYLINDER,- XCYLINDER, YCYLINDER, ilEMISPilERE, IIEMISPHE+X, HEMISPIIE-X,- HEMISPHE+Y, HEMISPHLY, .

IIEMISPHE+ Z, . HEMISPHE-Z, XHEMICYL+ Y, XilEMICY1-Y, .XHEMIOL Z, .

XHEMICYl-Z, - YHEMIGLX, YHEMICYI-X, :YHEMICYL+Z, YHEMICYI Z, ZilEMIGL X, ZHEMIGLX, ZHEMIQb Y, ZHEMIGLY Note:fgeom may be no more than 12 characters long.

, v v, y ~., [ .-,,v% 5 , <,e.., ~,x--, . , , , , , , , m-m-,m,m. _,..-%,4,..v., .,-,%#m.., , . _, ..m.,.-,-....,_4.-., .. ~.m.m.%.-~,m-

1711.4.13 C0110 has + X - 4 Y - + Z and X - Y - -Z. Note that the + X dimension need not equal the X dimension of the cube; i.e., the origin need not be at the center of the cube.

CUllOID is a rectangular parallelepiped and may be described anywhere relative to the origin.

Spill:HE mun be centered about the origin, unless otherwise specified by the optional region origin data.

CY1 INDI:H has its length described along the Z axis and its center line must lie on the Z axis, unless otherwise specified by the optional region origin data.

ZCYl.INDi.~ H has its length described along the Z axis and its center line must lie on the Z asis, unless otherwise specified by the optional region origin data.

XCY1.IN DER has its length described along the X axis and its center line must lie on the X axis, unless otherwise specified by the optional region origin data.

YCYl.INDI:H has its length described along the Y axis and its center line must lie on the Y axis, unless otherwise specified by the optional region origin data, lil3tlSPill'.RE is used to define a spherical segment of one base whose spherical surface exists in the positive z direction. The base or flat portion of the spherical segment is centered about a point that may be specified in the optional region data. Ily default, the center of the spherical surface is the origin and the distance to the base from the center of the spherical surface is 7ero.

Ps illSPilEbc is umi to define a spherical segment of one base whose spherical surface exists in the bc direction (b - + or , c - x, y or z). The base or flat portion of the spherical segment is located a distance p from the center of the spherical surface, and the center may be specified in the optional region data. IIEhtiSPilE+Z is the same as the previously described ilEMISPIIERE and llEMISPilE-Z is the mirror irange of IIEMISPilE+Z, therefore existing only in the negative Z direction.11y default the center of the spherical surface is the origin and the distance of the base from the center of the spherical urface is zero.

bilEhtlCYled is used to define a cylindrical segment whose axis is in the b direction (b - x, y, or z) and whose cylindrical surface exists only in the c direc .

tion from a plane perpendicular to the d axis (c - + or , d . x, y or z). The position of this planc (cut surface) can be specified in the optional region data. This plane cuts the cylinder parallel to the axis at some dis-tence, p, from the axis, lly default, the amis passes through the origin and p is zero. (Exarnples: ZllEMICYls X, YllEMICLZ, XIIEMICYla Y)

l Fila.14 4

The AI/X7URE 10 mat specifies the mixture that is to occupy the volurne defined by the region.

This is followed by one or more blanks.  ;

The B/AS 10 imp specifies the weights that are to be used in the volume defined by the reometry card. Default weights are used for every imp not specified in the B/AS/AO INFORA/ATlON data. For clarification of how to use imp to r specify nondefault weights, see Sect. Fil A.7. The BIAS /D number is ,

followed by one or more blanks.

APPROPRIATE REGION DIAfENSIONS lxx(I) through 22(6)) are scratated by one or more blanks and defme the site of the region. 1 xx(l) Radius for a sphere, cylinder, hemisphere, or hemicylinder,

+X dirnension for a cube or cuboid.

xx(?) .X dimension for cube or cuboid,

+Z for cylinder or Z cylinder,

+ X for X cylinder,

+ Y for Y cylinder, 4 length for hernicylinder, omit xx(?) for a sphere or hemisphere.

xx(3) +Y dimension for cuboid,

.Z for cylinder or Z cylinder,

.X for X cylinder,

.Y for Y cylinder, ,

. length for hemicylinder, omit xx(3) for a sphere, hemisphere, or cube.

xx(4) Y dimension for cuboid, omit for all other geometry types.

xx(3) + Z dimension for cuboid, omit for all other geometry types.

xx(6) .Z dimension for cuboid, omit for all other geometry types.

Enter origin data in the form:

fgcom enter the word ORIG or ORIGIN xx(l) the X coordinate of the origin of a sphere or hemisphere,-

the X coordinate of the centerline of a Z or Y cylinder or hemicylinder, the Y coordinate of the centerline of an X cylinder or hemicy!inder.

xx(2) _ the Y coordinate of the origin of a sphere or hemisphere, _

the Y coordinate of a Z cylinder or hemicylinder, the Z coordinate of an X or Y cylinder or hemicylinder.

xx(3) the Z coordinate of the origin of a sphere or hemisphere; omit for all cylinders _

and hemicylinders.

. , _ , _ _ _ . _ _ . _ . _ _ . ~ . _ _ _- _ _ - __ , _ - _ . ..

t Fi l .4.15 Enter chord data in the form:

fgom enter the word Cil0RD A2(7) The distance, p, from the ' cut surface

• to the center of the spherical surface or axis of a he>nicylinder. See il) and (2) atmvc and Firs. Fil.4.6 and Fil.4.7.

For example if p is 5 cm for both pictures, the chord data for Fig. Fil.4.6 would be Cil0RD $.0 and the chord data for Fig. Fil.4.7 would be Cil0RD 5.0. Entering a positive value with Cil0RD implies that more than half of the spherical or cylindrical body custs; entering a riegative value with C110RD implies that less than half of the spherical or cylindrical taly exists. i N

d  %

q -- I I

'\r P o t /

N.<!f :.:g 3;/ kN:

9: " y.T ,

Fif.. Fil.4.6. Partially filled hemisphere or hemicylinder less than half full OHNL-OWG B3 9726

,e N,

.Yh .: :{ P_h{hih h$*)iN.;U wg% "?SIflf'b MM/

t t

WO3R%.Wd?

.x&.? y; %

Fig. Fil.4,7. Partially filled hemisphere or hemicylinder more than half full .

Fila.!6 (c) EXTENDED GEOhfETRY DESCRIPTION . . . This type of geometry data references geo-metric description data from other geometry or array descriptions. Free form input is used to enter the data. Options R ', 5, and P from Table Fil.4.2 can be used. Each EXTENDED Gh0 METRY DESCRIPTION is entered in the form:

GEOAfETR P lt'ORD fgrom REFERENCEID mal BIAS ID imp THICKNESS PER REGION xx ORIGlN COORDINATES origin data GENERATED REGIONS ,

nerg The GEOAfETRP li'ORD fgrom is followed by one or more blanks and must be one of the keywords below.

ARRAY, CORF4 COREBDY, COREBNDS, COREBOUN, llOLE, REPLICATE -

HEFLECTOR NOTE: fgrom may be no more than 12 characters long.

ARRAY, CORE, COREBDY COREBNDS or COREBOUN are ARRAP PLACEAfENT descrip-tions. They always start a new unit and generate a rectangular parallelepiped that fits the outer bound-aries of the specified array. When an array placement description is the first geornetry region in a unit, the specified array is positioned in the unit according to its origin coordinates. The origin coordinates specify the most negative point in the array with respect to the coordinate system of the surrounding unit.

IIOLE is used to place a specified unit within the simple geometry region that precedes it. The position of the llOLE within the region is determined by the origin coordinates.

REPLICATE is used to generate additional geometry regions having the shape of the previous region. The geometry word REFLECTOR is a synonym for REPLICATE. The desired weighting func-tions can be applied to those regions by specifying biasing data as described in Sect. Fil.4.7. The REPLICATE specification includes (1) the AtlXTURE 10, mar, (2) the first BIAS ID, Imp, for which these weighting data apply, (3) the thickness per region for each surface, xx(l)...xx(6), as necessary to specify the desired thickness per region for each surface of the shape being generated, and (4) the num-ber of regions to be generated, nreg. The total thickness generated for each surface is the thickness per region for that surface times nreg.

Fila.17 The replicate card is frequently used to generate weighting regions external to the ARRA)' PLACE-AfENT description. Thus an ARRAl' PLACEAIENT description followed by a HEPLICATE descrip.

tion would generate regions of a cuboidal shape. A cylindrical tenector could be generated by following the ARRA)'PLACEAfENTdescription with a CYLINDER and then a HEPLICATE. A IlOLE cannot immaiately follow a HEPLICATE.

4 regions using default weights can be generated by specifying the first irnportance region, Imp, to be one that was not defined in the BIASING INFORAIATION. This capability can be used to gen-erste extra regions for collecting inforrnation such as Auxes, leakage, etc, Multiple replicate descriptions can be used in any problem. This can be utillied to handle different reDector materials of different thickness on different faces.

The nurnber of appropriate region dimensions, xx, for specifying REPLICATE are determined by '

the pieceding region. (For example, if the previous region was a sphere, one entry is required. If the previous region was a cylinder, the first entry is the thickness / region in the radial direction, the second entry is the thickness / region in the positive !cngth direction, and the third entry is the thickness / region in the negative length direction, etc.) The replicate specification requirements for a cube are the same as for a cuboid.

REFERENCE ID mar specifies (1), (2) or (3) below (1) numara, the array referenced by the ARRA)' PLACEAIENT r description ( ARRAY, CORE COREBDY, etc.) '

(2) thoir, the unit that is to be placed within the preceding SIAffLE GEOAfETR)" REGION for a 110LE description.

(3) mat, the mixture that is to be used in the generated regions for a REPLICATE description.

BIAS ID imp (1) omit if fream is ARRAY Enter a positive number for other ARRAl' PLACEAfENT descriptions.

(2) omit if fgrom is llOLE (3) For REPLICATE, imp is the BIAS 10 number corresponding to the first generated region and is incremented by one for each gen-erated region. If Imp is negative, it is not incremented, and all the generated regions use the absolute value of imp as their B/AS-ID.

APPROPR'"E REGION DIAIENSIONS \xx(l) through xx(6) ste separated by one or more blanks.

THICKNr'SS PER REGION xx (1) omit for ARRAl'PLACEAIENTdescriptions (2) omit for il0LE (3) for REPLICATE. [xx(l) through xx(6)] are separated by one or -

more blanks and define the site of the region. The thickness per region is always positive.

. _ ~

I Fil.4.18 2x(l) First thickness per region for the generated geometry (i.e., in the radial direction for i

a spherical or cylindrical shape, or in the positive X direction for a cube, cuboid or core), l x2(1) Second thickness per region for the generated geometry (i.e., in the direction of posi-tive length for a cylinder or hemicylinder or ' the negative X direction for a cube, cuboid or core).

Omit for sphere or hemisphere.

xx(3) Third thickness per region for the generated geometry (i.e., in the direction of nega-tive length for a cylinder or hemicylinder or in the positive Y direction for a cube, cuboid, or core).

Omit for sphere or hemisphere.

Fourth thickness per region for the generated geometry (i.e., in the negative Y direc-xx(4) tion for a cube, cuboid, or core).

Omit for all other geometry types.

xxt3) Fifth thickness per region for the Fenerated geometry (i.e.,in the positive Z direction for a cube, cuboid, or core).

Omit for all other geometry types.

x2(6) Sixth thickness per region for the generated Ecometry (i.e., in the negative Z direc-tion for a cube, cuboid, or core).

Omit for all other Ecometry types.

ORIGIN COORDINATES xxorg \xxorg(l) through xxorg(3) are separated by one or more blanks}

xxorg(l) (1) enter the X coordinate of the most negative point of the array with respect to the coordinate system of surrounding unit for ARRA)"fLACEAfENT descriptions (2) enter xhole, the offset in the X direction of the origin of the 110LE UNIT with respect to the origin of the region in which it is placed (3) omit for REPLICATE i

xxorg/2) (1) enter the Y coordinate of the most megative point of the array with respect to the sur-rounding unit for ARRAY PLACEAfLNT description l

(2) enter yhole, the offset in the Y direction of the origin of the ll0LE unit with respect to the origin of the region in which it is placed I (3) omit for REPLICATE xxorg(3) (1) enter the Z coordinate of the most negative point of the array with respect to the sur-rounding unit for array placement descriptions l

(2) . enter shole, the offset in the Z direction of the origin of the IIOLE unit with respect to the origin of the region in which it is placed -

(3) omit for REPLICATE -

)

.,- 'W^'"" mmc 5g y , , , ,_

Fil A.19 NUAfBER OF GENERATED REGIONS nreg (I) omit for array placement descriptions (2) omit for llOLE (3) enter the number of regions to be Fenerated for REPLICATE OPTIONAL. GEOAIETR)* COA /AIENTS these data allow the user to enter a comment for any unit. Data are entered in the form:

COM - delim coment delim The keyword COM-- signals that a comment is to be read. The first non. blank character following the keyword is the begmninF delimiter, delim. The comment can be as long as 132 characters, including imbedded blanks. It must be terminated with the same delimiter that signaled the beginning of the comment. The optional geometry comment rnust follow the UNIT INITIALIZATION for a unit but can precede or follow any SIMPLE or EXTENDED GEOMETRY REGION DESCRIPTION within '

the unit. In the event that more than one comment is entered within a unit, the last one is used. Exist-ing comtnents are printed at the beginninF of each unit description in the computer printout.

Ell A.5 ARRAY DATA ARRAY DEIINITION DATA . . The array dennition data block is used to define the site of an array and *e posit!on units (defined in the geometry data)in a three-dimensionallattice that represents the array being described. As many arrays as are necessary can be described in a problem, subject to computer storaEc limitations. A single unit problem is one for which an array definition data block is not entered.

An array definition data block consists of ARRA)' PARAAIETERS followed by a UNIT ORIEN.

TATION DESCRIPTION. The sequence ARRA)' PARAAfETERS, UNIT ORIENTATION DESCRIPTION must be repeated for each array that is to be used in the problem. ARRAY PARAAl-ETERS must be entered for all array problems and consist of parameter input defining (1) an array identification number for the lattice, (2) the number of units in each direction of the three-dimensional lattice, (3) the global array number, and (4) a comment to be printed at the beginning of the array in the printout. The global array is the array referenced by the global unit in a problem.

If there is no global unit, the global array is the outermost array in the description of the problem. The ,

array identification number, (1), and the number of units in each direction. (2), and the associated UNIT ORIENTATION DESCRIPTION must be critered for each array that is used in the problem.

The global array number (3), should be entered only if a global unit does not exist. If it is entered more than once, the last value is used. The optional array comment is available for the user's conven-ience, but is not necessary for the problem. The UNIT ORIENTATION DESCRIPTION consists of a eel'It'ORD. UNIT ORIENTATION DATA and a DELIAllTER which must be entered in order. The KE)'irORD is used to indicate _ the method of entering the unit orientation data. The UN/T ORIEN.

TATION DATA sequence is used to position units in thtee-dimensional lattice and the DEL /AflTER is used to terminate the unit orientation data for the array. The UNIT ORIENTAT/ON DESCRIPTION does not need to be entered for a problem in which only one box type or unit is described unless that

unit number is larger than 1, it must be enteredfor allproblems utilizing more than one unit or bos l

type. The adjacentfaces of units in contact with each other within an array must be the same size and -

shape. Multiple arrays are denned by entering the sequence ARRATPARAAIETERS, UNIT ORIEN-TATlON DESCRIPTION for each array that is to be described in the problem.

l Enter ARRAY DEFINITION DATA in the form:

. - . . _ . . . , _ , _ . . . . . _ _ . . . _ . , . - - - . . , , . . .,, .. __. r . . - - - _ _ , . . , _.

I l

FlI.4.20 RCAD ARRAY ARRA)* PARAAfETERS UNIT ORIENTATION DESCRIPTION END ARRAY l

A lx1xl array of Unit I can be defined by entering only the READ ARRAY END ARRAY, i ARRA)' PARAAIETERS define the array number and the array site. They utilire the following key.

words. Enter only those whose value you wish to change.

ARRAl' PARA AfETERS ARA = numa array number for the array being input, default - 1 Gill. - iglobl array nurnber for the global array (enter no more than once for a problem), default - largest value of numa for an unreflected system or the value of numara entered in the global unit, NUX . nb2 max number of units in the X direction of the array, default -I NUY - nbymar number of units in the Y direction of the array, default -1 NUZ - nb: max number of units in the Z direction of the array, default -I COM - delim coment delim allows entering a comment that will be printed with the unit orientation data. Maximum comment length is 132 characters.

• The UNIT ORIENTATION DESCRIPTION is composed of a KEkWORD. ORIENTATION DATA and a DELIAllTER as described below:

KE) WORD type enter the word LOOP or FILL, followed by one or more blanks.

LOOP enters unit orientation data in a manner resembling FORTRAN DO loops.

The first field contains the unit number, followed by three fields that are treated like FORTRAN DO loops. The arrangement of boxes may be considered as consisting of.

a three-dimensional matrix of unit numbers, with the unit position increasing in the positive X, Y, and Z directions, respectively. Each set of mixed box orientation data for the LOOP option consists of the following parameters, separated by one or more blanks.

\ ORIENTATION DATA for IDOP ltype The unit or box type,ltype must be greater than zero.

ixt The starting position in the X direction, fxl must be at least I and less than or equal to nbxmax (parameter NUX).

ix2 The ending position in the X direction,Ix2 must be at least I and less than or equal to abxmax.

! 11.4.21 inc2 The number of units by which increments are made in the positive X direction. incx must be greater than sero and less than or equal to nb2 max.

syl The startmr position in the Y direction. irl must be at least I and less than or equal to nbymas (parameter NU)')

ty? The ending position in the Y direction,iy2 must be at least I and less than or equal to nbymax.

incy The number of boxes by which increments are made in the positive Y direction, incy must be greater than zero and less than or equal to nbymas.

/ The starting position in the Z direction i:/ must be at least I and less than or equal to nb: max (parameter NUZ). -

i:2 The ending position in the Z direction,i:2 must be at least I and less than or equal to nh: max.

inc: 1he number of txnes by which increments are made in the positive Z direction. inct must be greater than zero and less than or equal to nb: mar.

The sequence h)/e through inc: is repeated until the entire array is described. if any portion of an array is defined in a conflicting manner, the last entry to define that portion will determine the array's confiFuration. To utilite this feature, fill the entire array with the most prevalent unit type and super.

impose the other unit types in their proper places. An example showing the use of the IX)OP option is given below.

Giien:

12121 21212 1ili1 11111 22222 13331 11111 22222 13331 -

12121 21212 1111I Z Layer 1 Z Layer 2 Z Layer 3 The data for this array could be entered using the following entries:

(1) 1 I$I I41 131 This fills the entire array with l's.

(2) 2 252 143 111 This loads the four 2's in the first layer.

(3) 2 151 231 221 This loads the second and third rows of 2's in the second layer.

(4) 2 152 143 221 This loads the desired 2's in the first and fourth rows of the second layer.

(5) 3 241 231 331 This loads the 3's in the third layer and completes the data input for the array.

Fi 1.4.22 The second layer could have been defined by substituting the following data for entries (3) and (4).

(3) 2 1$I i41 221 This completely fills the second layer with 2's.

(4) I 242 143 22i This loads the four l's in the second layer, When using the LOOP option, there is no single correct method of entering the data. If a unit is improperly positioned in the array or if some positions in the array are left undefined,it is often easier to add additional data to correctly define it than to try to correct the existing data.

FILL enters deta by stringing in unit numbers starting at X-1, Y-1, Z 1, and varying X, then Y, and then Z to fill the array, nbxmax x nbymax x nb: max entries are required. FIDO like input options are also available for filling the array.

ORIENTATION DATA for FILL The FILL option consists of entering a unit number for every position in the array by using the FIDO like input options specified in TableFil.4.2. The orientation data for the FILL option may be terminated with a T.

DELIMITER Enter the word END followed by a blank and the previously entered KEYWORD (i.e., enter END FILL or END LOOP). The delimiter need not be entered if only one set of ARRAF DEFINIT /ON DATA is to b: read.

t:

FI l.4.23 Table Fil.4.2. FIDO like input for mixed box orientation fill option Count Option Operand Field Field Field Function j stores j at the current position in the array i R j stores j in the next i positions in the array

/ '

] stores j in the next i positions in the array

/ 5 j stores f in the next i positions in the array I p j alternately storesj - nd )in the next I positions of the array F j fills the remainder of the array with unit number j, starting with the cur-rent position in the array A j sets the current position in the array toj i S increments the current position in the array by i (This allows skipping i positions. I may be positive or negative.)

i Q j repeats the previous j entries i times. The default value of f is 1.

I N j repeats the previous j entries i times, inverting the sequence each time, The default value of f is 1.

I D j back i entries. From that position, repeat the previous j entries in reverse order. See Exampic 4. The default value of i is 1.

I I JA provides i entries linearly interpolated between j and k, and the'end points (i.e., a total of i+2 points)J and k must be separated by at least one blank.

i L jk provides i entries logarithmically interpolated between j and k, and the end points (l.c., a total of i+2 points) J and k must be separated by at least one blank.

T terminates the data reading for the array When entering data utilizing the options in this table, the countfield and optionfield must be adjacent

- with no imbedded blanks, The operand field may be separated from the option field by one or more blanks.

~- .

Fi 1.4.24 To illustrate the use of the options available in Table Fil.4.2, consider the following examples The positions in an array are numbered sequentially from left to right, bottom to top. A 3x3x1 array is numbered as shown below.

7 F 9 4 5 6 1 2 3 EX AMPLE 1. Consider a 3x3x1 array filled as shown below.

1 I i 1 2 1 1 1 1 The input data to describe this array coukt be entered as follows:

(1) Ii1121111T This fills the array, one position at a time, starting at the lower left corner. The T terminates the data.

(2) Fl A5 2 T The F1 fills the entire array with il the A5 locates the fif/h posi-tion in the array, and the 2 loads ,. 2 in that position. The T ter-minates the data.

(3) FI At 4S 2 T The F1 fills the entire array with I's, the Al locates the first position in the array (lower left corner), the S4 skips over the next four posi-tions in the array, and the 2 loads a 2 in the next position. The T terminates the data.

(4) 4R12 4RI T The first 4R1 loads l's in the first four positions of the array, a 2 is lo + i :n the next (fifth) position of th array, and the last 4R1 I acs l'a .a the next four positions of the array. The T terminates tL car (5) 4'l 2 451 T The 4*1 load, l's in the first four positions of the array. A 2 is loaded in the next position of the array, and the 451 loads l's in the next four positions of the array. Th; T terminates the data.

EXAMPLE 2. Consider a 4x3x1 array filled as shown below.

I 2 2 1 1 2 2 1 1 2 2 1 i

I

. - . . ,. . . - - - - . - . = -

Fi 1.4.25 The input data to d: scribe this array could be entered as follows.

(1) I 2 2112 2112 21 T This fills the array, one position at a-time, starting at the lower left corner, The T terminates the data.

(2) 12R2 2RI Q4 2R21 T A I is loaded in the first position of the array. The 2R2 loads 2's in the next two positions of the array (positions two and three). The 2R1 loads l's in the next two positions of the array (positions four and five). The Q4 loads the 2 21 i from positions: two through five in positions six through nine. The last 2R2 loads 2's in positions ten and eleven of the array. The last I loads a 1 in the next' position (position twelve). The T terminates the data.

(3) 12 SN2 T The 1 is entered in the first position of the array and the 2 is entered in the second position. The SN2 causes the previous two entries to be repeated five times, reversing their order each time. The T terminates the data.

(4) 12R212Q4 T The first 1 is loaded in the first position of the array. The 2's are loaded in positions two and three of the array. Then a 1 is' loaded in the fourth position of the array. This describes the entire bottom row of the array. The 2Q4 then repeats the previous four entries (those loaded in positions one through four of the array) two times. Thus the first row is repeated twice, filling th. remainder of the array.

EA Conside . t.x3x1 array as shown below.

1 I 2 s

1 2 2 1 1 2 1 2 2 1 1 2 A simple input description for this array is:

(1) 12 2N2 2Q6 T The first position of the array is filled with a 1. ,The second position of the array is filled with a 2. The 2N2 causes the previous two entries to be repe ted two times, reversing their-order each time. This completes loading the bottom row of the array. The 2Q6 repeats the previous six entries twice, completing the second and third rows of the array. The T terminates the data.

EXAMPLE 4. Consider a 7x3x1 array as shown below.

I 2 3 4 3 2 1 2 3 4 5 4 3 2 1 2 3 4 3 2 1

• yr q

4 Fil A.26

~

The input date to describe this array could be entered as follows:

(1) 1.2 3 4 IB3 2345183 12 3 4 IB3 T The 12 3 and 4 are loaded in the' first four positions of the . array. The IB3 steps back over the 4 and repeats the 12 3 sequence in reverse order (i.e., 3 2 l). This yields the 1234321 in the first row of the array.

The same procedure applies to the next two rows.

(2) 1234183 23451810 T The 1 234 IB3 yields the first row as explained above. The 2 3 4 5 -enters the 2 3 4 5 at the left of the second row. The 1B10 enters the 4 3 2 at the right of the second row and the entire third row.

Fi l.4.6 ALBEDO DATA ALBEDO DATA . . Albedo boundary conditions are entered using a FACE CODE to define where albedo conditions are to be used, and an ALBEDO NAME to indicate which albedo condition is to be used on that face. The default valce for each face is vacuum. The default values are overridden -

only on faces for which other albedo names are specified. Albedo boundary conditions are applied only to the outermost region of a problem. This geometry region must be a rectangular parallelepiped.

Enter ALBEDO DATA in the form:

READ BOUNDS FACE CODE face

ALBEDO NAAfE aname END BOUNDS The sequence FACE CODE, ALBEDO NAAIE is entered as many times as necessary to define the appropriate albedo boundary conditions. If multiple entries are made for a face, the ALBEDO NAAIE associated with the last FACE CODE specifying that face is used.

The FACE CODES are described in Table Fil.4.3 and the ALBEDO NAAfES are given in Table Fi l .4.4.

1

. ~ . _ . .

Fl 1.4.27 Table Fil A.3. Face codes for entering boundary (albedo)' conditions Face Code Faces that are defined by the Face Codes ,

+XB- positive X face

&XB- positive X face

.X B . negative' X face

+YB- positive Y face

&YB- positive Y face

-YB. negative Y face 4ZB. positive Z face

&ZBa positive Z face

-ZB- regative Z face ALL- all 6 faces XFC- both positive end negative X faces YFC- both pc:,-'.ive and negative Y faces ZFC- both positive and negative Z faces

+FC- positive X, Y, and Z faces

&FC- positive X, Y, and Z faces

-FC - negative X, Y, and Z faces XYF- positive and negative X and Y faces XZF- positive and negative X and Z faces YZF- positive and negative Y and Z faces

+XY- positive X and Y faces

+YX- positive X and Y faces

&XY- positive X and Y faces

&YX- positive X and Y faces 4XZ- positive X and Z faces

+ZX- positive X and Z faces

&XZ- positive X and Z faces

&ZX=- positive X and Z faces

+YZ- positive Y and Z faces

+ZY- positive Y and Z faces

&YZ- positive Y and Z faces

&ZY- positive Y and Z faces

-XY- negative X and Y faces XZ- negative X and Z faces YZ- - negative Y and Z faces YXF= positive and negative X and Y faces ZXF- positive and negative X and Z faces ZYF. positive and ne;;ative Y and Z faces YX - negative X and Y faces ZX- negative X and Z faces ZY- negative Y and Z faces

. _ . = -

Fi 1.4.28 -

4 Table Fl1.4.4. Albedo names available on the KENO V albedo library for use with the face codes -

Albedo Name Albedo Description DP01120 12 in. (30,48-cm) double P. water differential DPOll2O albedo with 4 incident angles -

DP0

?

DPO -7 112 0 12-in. (30.48 cm) water differential albedo  ;

WATER - with 4 incident angles PARAFFIN 12-in. (30.48-cm) paraffin differential albedo PARA with 4 incident angles WAX CARBON 78.74-in. (200.00 cm) carbon differential GRAPlilTE albedo with 4 incident angles C

ETIIYLENE 12-in. (30.48-cm) polyethylene differential POLY albedo with 4 incident angles Cil2 CONC-4 4-in. (10.16-cm) concrete differential albedo CON 4 with 4 incident angles CONC 4 CONC-8 8-in. (20.32-cm) concrete differential albedo CON 8 with 4 incident angles CONC 8 CONC 12 12-in. (30.48-cm) concrete differential albedo CON 12 with 4 incident angles CONCl2 CONC 16 16-in. (40.64 cm) concrete differential albedo CON 16 with 4 incident angles CONC 16 CONC 24 24-in. (60.96-cm) concrete differential albedo CON 24 with 4 incident angles CONC 24 VACUUM vacuum condition VOID VACU VAC SPECULAR mirror image reflection MIRROR-MIRR SPEC SPE MIR REFL-REFLECT PERIODIC ~ periodic boundary condition PERI PER

Fii A.29 Fil A.7 BIASING OR WEIGIITING DATA BIASING INFORMATION . , , The average weight of a neutron that survives Russian roulette,

• wravg, is defaulted to dwtav (%TA= in the parameter data) for all BIAS ID's and can be overridden -

by entering biasing information.

The biasing information is used to relate a BIAS /D to the desired energy-dependent vLlues_ of wtavg. This concept is similar to the way the M/XTURE ID, mat is related to the macroscopic cross-section data.

The weighting functions used in KENO V are energy-dependent values of wtavg that are applicable over a given thickness interval of a material. For example, the weighting function for water2 is com-posed of sets of energy-dependent values of wtavg for 11 intervals, each interval being 3 cm thick. - The first set of wtavg's is for the 0 to 3-cm interval of water, the second set of wravg's is for the 3 to 6-cm interval of water, etc. The eleventh set of wravg's is for the 30 to 33-cm interval of water.

To input biasing information, a BIAS ID must be assigned to correspond to a set of wravg. Biasing data can specify a MATERIAL ID from the existing KENO V weight library or = from the AUX /LIARY DATA input. The materials available from the KENO V weights library are listed in Table Fl1.4.5.

BIASING INFORMAT/ON is entered in the following form:

READ BIAS KEYWORD CORRELATION DATA AUXILIARY DATA END DATA KEYWORD enter ID=, %T. or MTS=

ID- specifies that CORRELATION DATA will be entered next.

%T= or WIS= specifies that AUX /L/ARY DATA will be entered next.

CORRELAT/ON DATA are used to correlate a set of wtavg to a BIAS ID, imp, as specified in the geometry data. This causes the specified wravg .

to be used as the weighting function in the volume defined by -

that geometry region.

CORRELATION DATA must be entered in the order shown, id entor the identif!:ation (MATERIAL ID) for the material whose weighting function is to be used. A material ID can be chosen from the existing KENO V weights library .

(Table Fil.4.5) or from the AUXILIARY DATA as described later. _ If a material ID appears in both the KENO V weights library and the AUXILIARY DATA, the wtavg from the auxiliary data will be used.

ibgn is the BIAS ID of the weighting function for the first interval of material id. The geometry card having imp - ibgn will use the group-dependent wtavg's from the first interval of material id.

iend. is the BIAS ID of the group-dependen; wtavg's from the (icnd - lbgn + 1)th inter"al-of materialId.

l Fi1.4.30 4

AUX / LIAR)' DATA are used to enter biasing or weighting information from cards.

It can be used to supply biasing information for materials not found in the KENO V weights library or to override the wtavgs from that library.

AUX / LIAR)' DATA must be entered in the order shown.

wititt enter an arbitrary 12 character title name such as CONCRETE, WATER, SPECI Alll20, etc., to identify the material for which you are entering data.

id enter an identification number (MATERIAL. ID). The value is arbitrary. Ilowever, if the data are to be utilized in the problem, this ID must also be used at least once in the CORRE:LATION DATA.

nsets enter the number of sets of group structures for which wtavg will be read for this id.

The sequence thAinc, numinc, ngpwt. wtarg, described below, is repeated nscis times.

shlinc enter the thickness of each increment for which wtavg will be read for this id.-

numinc enter the number of increments for which wtavg will be read for this id.

ngpwt enter the number of energy groups for this set of wtavg.

wtavg enter numinc n ngpwt values of wtavg. For each value of numinc, ngpwt values of wtavg must be supplied.

CAUTIONS:

1. Each act of auxiliary or correlation data must be completely described in conjunction with its key-wntd. Complete sets of these data can be interspersed in an arbitrary order but data within each set must be entered in the specified order.

2. Auxiliary data: If the same id is specified in more than one set of data, the last set having the -

group structure used in the problem is the set that will be utilized,

3. Correlation data: . If biasing data define the same bias ID (imp, from the geometry data) more than once, the value that is entered last supersedes previous entries. Re well aware that multipic definitions for the same bias ID con cause erroneous answers due to overbiasing. Error messages K5-125 and K5128 may be printed.

An example of multiple definitions for the same bias ID is given below:

READ BIAS ID=400 2 7 ID=500 $ 7 END DIAS The data for paraffin (ID.400) will be used for bias ID's 2, 3, and 4, and the data for water i (ID. 500) will be used for bias ID's 5,6, and 7.

?

4

Fi l.4.31 ,

- Multiple definitions for the same bias ID are not necessarily incorrect. Ilowever, the user should be cautious about doing it and assure that the desired biasing or weighting functions are utilized in the desired geometry regions. .

Table Fil,4.5, ID's, group structure and incremental thicknesses for weighting data available on the weighting library Group Structure Increment' Material For Which Weights Thickness - Total Number of Material ID Are Available (cm) increments Available Concrete 301 16 5 20 27 -5 20 123 5 20 Paraffin 400 16 3 10 27 3 11 123 3 10 Water 500 16 3 10 27 3 11 123 3 10 218 3 11 Graphite 6100 16 20 6 27 20 10 123 20 6

• Group-dependent weight averaSes are supplied for each increment of the specified incremental thickness, i.e., . for any given material, the first ngp (number of energy groups) weights apply to the first increment of-the thickness specified in Table Fil.4,4, the next ngp weights apply i to the next increment of that thickness, etc. CAUTION: If bias id's defined in the weighting information data are used in the geometry, the region thickness should be consistent with the incremental thickness of the

, weighting data in order to avoid over biasing or under biasing, i

l An example of how the BIAS ID relates to the energy-dependent values of wtavg is given below.

L Assume that a paraffin reflector is to be used and it is desirable to use the weighting function from l the KENO V weighting library to minimize the running time for the problem. Also assume that these weighting functions are to be used in the volumes defined in the geometry cards having imp- 6,7,8, i and 9. CORRELATION DATA are then entered.

f KE1 WORD is ID.

id is 400, the ID for paraffin ibgn is 6, the first imp that uses the weighting function tend is 9, the last imp that uses the weighting function l

1 i

,w-

Fi l.4.32 and AUXIL/ARY DATA will not be entered. The biasing data would be: READ BIAS,lD-400 6 9 END BIAS -

The results of these data are:

(1) the group. dependent wtavg for the O to 3-cm interval of paraffin will be used in the volume defined by the geometry card having imp. 6.

(2) the group-dependent wravg for the 3 to 6-cm interval of paraffin will be used in the volume defined by the geometry card having imp- 7.

(3) wravg for the 6 to 9 cm interval of paraffin will be used where imp. 8.

(4) wravg for the 9 to 12-cm interval of paraffin will be used where imp- 9.

Fi l.4.8 START DATA START DATA . . Special start options are available for controlling the initial neutron distribu-tion. The default starting distribution for an array is flat over the overall array dimensions, in fissile material only. The default starting distribution for a single unit is flat over the system, in fissile mate-rial only. See Table Fil.4.6 for the starting distributions available in KENO V.

READ START The starting information that can be entered is given below. Enter only the data necessary to describe the desired starting distribution.

NST- nrypst start type, default - 0 See Table Fil.4.6 for available options.

TFX- ifx the x coordinate of the point at which neutrons are to be started, default- 0.0 Use for start types 3,4, and 6.

TFY- tfy the y ,:oordinate of the point at which neutrons are to be started, default- 0.0 Use for start types 3,4, and 6.

TFZ- If: the z coordinate of the point at which neutrons are to be started, default- 0.0 Use for start types 3,4, and 6.

i i

1 i

'l

' Fi l .4.33

1 Table Fil.4.6. Starting distributions available in KENO Y , j i

Start Required Optional _

Type Data - Data Starting Distribution 0 None NST Uniform throughout fissile material within the volume XSM defined by (1) the outer region of a single unit,(2) the XSP outer region of a reflected array having the reflector YSM key set true, (3) the core boundary of the global array, YSP or (4) a cuboid specified by XSM, XSP, YSM, YSP, ZSM, ZSM and ZSP.

Z%P RFL PSP 1 NST XSM The starting points are chosen according to a cosine XSP distribution throughout the volume of a cuboid defined YSM XSM,- XSP, YSM, YSP, ZSM, and ZSP. Points that are not YSP in fissile material are discarded.

ZSM ZSP RFL PSP 2 NST XSM An arbitrary fraction (FCT) of neutrons are started NXS XSP uniformly in the unit located at position NXS, NYS, NYS YSM . NZS in the global array. The remainder of the NZS YSP neutrons are started in fissile material, from FCT ZSM points chosen from a cosine distribution throughout-ZSP the volume of a cubo;d defined by XSM, XSP, YSM, YSP,-

RFL ZSM, ZSP.

PSP 3 NST KFS All neutrons are started at position TFX, TFY, TFX PSP TFZ within the unit located at position TFY NXS, NYS, NZS in the global array.

TFZ NXS NYS NZS 4 NST KFS All neutrons are started at position TFX, TFY, TFX PSP TFZ within units NBX in the global array.

TFY TFZ NBX 5- NST PSP Neutrons are started uniformly in fissile NBX- material in units 'IBX in the global array.

6 NST NXS The starting distribution is arbitrarily input. LNU TFX ' NYS - is the final neutron to be started at a point TFX, TFY NZS TFY, TFZ relative to the global coordinate TFZ KFS system or at a point TFX, TFY, TFZ, relative LNU' PS6 to the unit located at the global array PSP position NXS, NYS, NZS.

• When entering data for start 6, LNU must be the last entryfor each set of data and the LNU in each successive set of data must be larger than the last. A set of data consists of required and optional data.

The last LNU entered should be equal to the number per generation (parameter NPG in the parameter input),

Fi l.4.34 NXS- nbxs the x index of the unit's position in the global array, default = 0 ^

Use for start types 2,3, and 6, NYS- nbys the y index of the unit's position in the global array, default -0 Use for start types 2,3, and 6.

NZS- nbrs the z index of the unit's position in the global array, default - 0 Use for start types 2,3, and 6.

the mixture whose fission spectrum is to be used for starting neutrons that are not .in a KFS- Afis fissionable medium. Defaulted to the first fissionable mixture. Available for natt types 3,4, and 6.

the final neutron to be started at a point. Default - 0. Each lfin should be greater LNU- Ifin than zero and less than or equal to NPG.

Use for start type 6.

NIlX- nboxsr the unit or box type in which neutrons will be started. Default - 0 Use for start types 4 and 5.

FCT- fract the fraction of neutrons that will be started as a spike. Default -0 Use for start type 2.

XSM- xsm the -X dimension of the cuboid in which the neutron will be started. For an array problem, XSM is defaulted to the minimum X coordinate of the global array.- If the reflector key RFL is YES, and the outer reflector region is a cube or cuboid, XSM is defaulted to the minimum X coordinate of the outer reflector region. If RFL is YES and the outer region of the reflector is not a cube or cuboid, XSM must be entered in the data and must fit inside the outer reflector region. Available for start types 0,1, and 2.

XSP- xsp the +X dimension of the cuboid in which the neutrons will be started. For an array problem XSP is defaulted to the maximum X coordinate of the global array. If the reflector key RFL is YES, and the outer reflector region is a cube or cuboid, XSP is defaulted to the maximum X coordinate of the outer reflector region. If RFL is YES and the outer region of the reflector is not a cube or cuboid, XSP must be entered in the data and must fit inside the outer reflector region. Available for start types 0,1,-

and 2.

YSM- ysm the -Y dimension of the cuboid in which the neutron will be started. For an array problem YSM is defaulted to the minimum Y coordinate of the global array. If the reflector key RFL is YES, YSM is defaulted to the minimum Y enordinate of the outer reflector region, provided that region is a cube or cuboid. If RFL is YES and

.the outer region of the reflector is not a cube or cuboid, YSM must be entered in the data and must fit inside the outer reflector region. Available for start types 0,1, and 2.

Fi l.4.35 YSP- yxp the + Y dimension of the cuboid in which the neutrons will be started. For an array problem YSP is defaulted to the maximum Y coordinate of the global array, if the reflector key RFL is YES, YSP is defaulted to the maximum Y coordinate of the outer reflector region, provided that region is a cube or cuboid. If RFL is YES and the outer region of the reDector is not a cube or cuboid, YSP must be entered in the data and must fit inside the outer reflector region.

Available for start types 0, I, and 2.

ZSM- :sm the Z dimension of the cuboid in which the neutrons will be started. For an array problem ZSM is defaulted to the minimum Z coordinate of the global array. If the renector key RFL is YES, ZSM is defaulted to the minimum Z coordinate of the outer reDector region, provided that region is a cube or cuboid. If RFL is YES and the outer region of the reflector is not a cube or cuboid. ZSM rnust be entered in the data and must fit inside the outer reflector region. '

Available for start types 0,1, and 2.

ZSP- :sp the +Z dimension of the cuboid in which the neutrons will be started. For an array problem ZSP is defaulted to the maximum Z coordinate of the global array. If the reflector key RFL is YES, ZSP is defaulted to the maximum Z coordinate of the outer reflector region, provided that region is a cube or cuboid. If RFL is YES and the outer region of the reflector is not a cube or cuboid, ZSP must be entered in the data and must fit inside the outer reflector region.

Available for start types 0,1, and 2.

RFL- rf7Acy the reflector key. If the reflector key is YES, neutrons can be started in the reDector, if it is NO, all the neutrons will be started in the array. Enter YES or NO.

Default - N O.

Available for start types 0,1, and 2.

PS6- /ptr6 the key for printing start type 6 input data. If the key is YES, start type 6 data is printed. If it is NO start type 6 data is not printed. Enter YES or NO.

Default - N O.

Available for start type 6.

PSP- Ipstp the key for printing the neutron starting points using the tracking format. If the key is YES, print the neutron starting points. If it is NO, do not print the starting points.

Enter YES or NO. Default - N O.

Available for all start types.

END START Fi l.4.9 EXi'RA 1-D XSECS ID'S DATA EXTRA 1-D CROSS SECTION ID'S Extra 1-D cross-section ID's need not be entered. They are allowed as input in order to simplify future modifications to calculate reaction rates, etc.

RE:D XIDS EXTRA l-D CROSS SECT 10N ID'S END X1DS

~_

Fi l.4.36 EXTRA 1-D CROSS SECTION ID'S Enter a 1-D identification number for each extra 1-D cross section to be used. These cross sections must be available on the mixture cross-section library, X1D entries are expected to be read (see integer PARAMETER data).

Fil.4.10 MIXING TABLE DATA CROSS SECTION MIXING TABLE . A cross-section mixing table must be . entered if KENO V is being run

• stand alone" and a premixed ICE tape is not being used. A cross section mixing table is entered in the form:

READ MIXT XSEC PARAAfETERS MIXIVG TABl.E END MIX 3 The XSEC PARAAIETERS include the number of scattering angles and the cross section message cutoff valut, The number of scattering angles specifies the number of discrete scattering angles to be used for the cross sections. It needs to be entered only once for a problem. If more than one value is entered, the last one is used for the problem. For assistance in deter-mining the number of discrete scattering angles for the cross sections, sec  ;

Sect. F11.5.4.3.

S C T nscr where nsct is the number of discrete scattering angles, default - 1 The cross-section message cutoff value is the value of the Po cross section for each energy transfer above which cross.section processing warning messages will be printed. The pri-mary purpose of entering this cutoff value is to suppress printing these messages when they are gen rated during cross-section processing. For assistance in determining a value .

' for EPS, see Sect. Fil.5.4.7.

!' EPS- pbxs where pbxs is the value of the Po cross-section for each transfer, above which generated warning messages will be printed, default - 3 x 10~5 The AflXING TABLE is used to specify each mixture and the nuclide ID's and number densities used in the mixtures. It consists of (a) a AIIXTURE ID and a set of (b) NUCLIDE ID's and (c) NUAfBElt j DENSITIES (atoms / barn-cm).

(a) AllXTURE ID MIX - mix where mix defines the mixture being described I'  ;

(b) NUCLIDE ID nuct enter the nuclide ID number from the AMPX working library

(c) NUAIBER DENSITY dens enter the number density associated with nuclide ID number nucl REPEAT the sequence (b) (c) until the mixture has been completely described.

REPEAT the sequence (a)(b)(c) until all the mixtures have been described.

1 NOTE: If a given nuclide ID is entered more than once in the same mixture, the number densities for that nuclide are effectively summed.

1

.-,,--w, -. - - , - , -- , ,, ,a., , , a--,w,, a-~

_ _ = _

Fil A.37 If a mixture number is used as a nuclide ID, it is treated as a nuclide and the number density asmciated with ;t is really a density modifier. (if the density is entered as 1, the mixture is mixed in at full density, if it is entered as 0.5, the mixture is mixed in at 1/2 its full density.) A Monte Carlo formatted cross section library is generated on the unit defined by the parameter XSC., if this data set is saved, subsequent cases can utilize these mixtures without remixing.

Fila.ll Pl.OT DATA PLOT or PICTURE DATA . . Printer plots or pictures of slices through the geometry cari be printed showing mixtures number, unit numbers, or bias ID nurnbers. The Pl.OT DATA can include the data for any or all types of pictures. A picture by mixture number is the default kind of picture.

The kind of picture is defined by the parameter PIC=. Printet plo!.s are printed after the volumes are prmted und before the final preparations for tracking are completed. Pl '71 DATA is not required for a problem but can be used to verify the problem descriptiran. The actual printing of the plot or picture can be suppressed by entering PLT- NO in the parameter data or picture data. This allows picture data to be kept in the problem data for reference purposes without actually printing the picture (s).

Entering a value for PLT in the picture data will override any value entered in the parameter data, llowever, if a problem is restarted, the value of PLT from the pararneter data is used.

Enter PLOT DATA in the form:

READ PLOT PICTUPE PARAhfETERS END PLOT P/C?URE PARAAfETERS are er,erca using keywords followed by the appropriate data. The plot title and the plot character string must be contained within delimiters. As many picture parameters as are necessary to describe the plot should be entered. The parameter input for each plot is terminated by an END.

Data for multiple plots are separated by the terminator END.

TTL- delim prirl delim enter a one-character delimiter delim to signal the beginning of the title (132 characters maximum). The title is terminated when delim is encountered the second time.

default - title of the KENO case PIC- wrd The picture type, wed, is followed by one or more blanks and must be one of the keywords listed below. Initialized to MAT; default = value from previous plot.

e

F11.4.38 MAT '

MIX' These keywords will cause the printer plot to MIXT represent the mixtures of mixture numbers MIXTURE I, ni the specified geometry slice.

l MEDI MEDIA BOX BOXT These keywords will cause the printer plot to BOXTYPE (represent the units or box types in the UNT I specified geometry slice.

UNIT UNITTYPE ,

IMP ,

BIAS BIASID i These keywords will cause the prSter plot WTS ito represent the Dias ID numbers used in I

WEIG the specified geometry slice.

WEIGHTS WGT WGTS Upper left coordinates enter the X, Y and Z coordinates of the upper left-hand corner of the plot.

Data must be entered for all three coordinates unless all three values from the previous plot are to be uwd.

XUL- fnam(l) enter thc.X coordinate of the upper left-hand corner of the plot.

default - value from previous plot; initialized to zero if any other coordinates are entered YUL- fnamf2) enter the Y coordinate of the upper left hand corner of the plot, default - value from previous plot; initialized to zero if any other coordinates are entered ZUL fnam/3) enter the Z coordinate of the upper left-hand corner of the plot.

default - value from previous plot; initialized to zero if any other coordinates are entered Lower right coordinates enter the X, Y, rad Z coordinates of the lower right-hand corner of the plot. Data must oe entered for all three coordinstes unless all three values from the previous plot are to be used. I l

XLR- fnam(4) enter the X coordinate of the lower right-hand corner of the plot.

default - value from previous plot; initialized to zero if any other coordinates are entered i

i

l Fi 1.4.39 q

, 1 YLR- fnam/5) enter the Y coordinate of the lower right hand corner of the plot, default - value from previous plot; initialized to zero if any other coordinates are entered ZLR. fnam(6) enter the Z coordinate of the lower right hand corner of the plot, default - value from previous plot; initialized to zero if any other coordinates are entered Direction cosines across the page - enter direction numbers proportional to the direction cosines' fon the AX axis of the plot. The AX axis is from left to right across the page, if any one of the AX direction cosines are entered, the other two are set to zero. The direction cosines are normalized by the code.

U AX. fnam(7) enter the X component of the direction cosines for the AX axis of the plot.

default = value from previous plot; initialized to zero if any other direction cosines are entered VAX= fnam(8) enter the Y component of the direction cosines for the AX axis of the plot.'

default - value from previous plot; initialized to zero if any other direction cosines are entered WAX. fnam/9) enter the Z component of the direction cosines for the AX axis of the plot, default - value from previous plot; initialized to zero if any other direction cosines; are entered Direction cosines down the page enter direction numbers proportional to the direction cosines for

~

the DN axis of the plot. The DN axis is from top to bottom down the page. If any one of the DN direction cosines are entered, the other two are set to zero. The direction cosines are normalized by the code.

- UDN--fnam(10) enter the X component of the direction cosines for the DN axis of the plot.

default - value from previous plot; initialized to zero if any other direction cosines are entered VDN- fnam(ll) enter the Y component of the direction cosines for the DN axis of the plot.

defau:t - value from previous plot; initialized to zero if any other direction cosines are entered -

WDN-fnam(12) enter the Z coniponent of the direction cosines for the DN axis of the plot, default - value from previous plot; initialized to zero if any other direction cosines

-are entered -

4 DLX- fnam(13) horizontal spacing between points on the plot. ~

- default - value from previous plot; initialized to zero if NAX or NDN is entered

.- ~ _ - - .

1 I

\

l F11.4.40 - l DLD fnam(14) vertical spacing bet-cen points on the plot. i default... value from previous plot; initialized to zero if NAX or NDN is entered ,

NOTE: If either DLX or DLD is entered, the code will calculate the value of the other. if both are entered, the plot may be distorted.

NAX- inam(13) number of intervals to be printed across the page, default - value from previous plot; initialized to zero if DLX or DLD is entered NDN- inam(16) number of intervals to be printed down the page, default - value from previous plot; initialized to zero if DLX or DLD is entered NOTE: If either NAX or NDN is entered, the code will calculate the value of the other. If both are entered, the plot may be distorted. If the coordinates of the lower right hand corner have been -

entered, only one item of (DLX, DLD, NAX, NDN) need be entered. If the coordinates have not been entered, it is necessary to enter both NAX and NDN in addition to either DLX or DLD. If the coordinates and NAX or NDN are entered, then DLX and/or DLD will be recomputed.

LPl= inam(17) number of lines per inch that will be printed down a page default - 8 NCH- delim CHAR delim enter a one-character delimiter to signal the beginning of a character string, CHAR. The character string is_ terminated when delim is encountered the second time. CHAR is a character string with each -

entry representing a media (mixture) number or unit number. These are the characters ihat will be used in the plot. The first entty represents media, unit or bias ID zero; the second entry represents the smallest media, unit or bias ID used in the problem; the third, the next larger media, unit or bias ID used in the problem; etc.

~lhe default values of CHAR are:

MEDIA o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15-SYMBOL 1 2 3 4 5 6 7 8 9 A b C D E F MEDIA 31 32 33 34 35 36 37 33 39 40 41 42 43 44 45 46 SYMBOL V W X Y 2- # 5 + )

.t > ,

MEDIA 16 17 18 14 20 21 22 23 24 25 26 27 28 29 30 SYMBOL G 11 I J K L M N O P Q R' S T U MED:A 47 43 49 50 51 32 53 54 - 55 56 57 3a SYMBOL - 9 * =  ! t e < , O a

e

Fi l.4.41 RUN. fnam(19) enter YES or NO. A value of YES means the problem will be executed if all the data were acceptable. A value of NO specifies the problem will be terminated {

after data checking is completed. The default value of RUN is YES. The value  ;

entered in the plot data will override the _v81ue entered in the parameter data, l Sect. Fil.4.3, unless the problem is being restarted, j PLT fnam/20) enter YES or NO. A value of YES specifies that a plot is to be made, if plot data l

are entered, PLT is defaulted to YES. If it is desirable to retain the plot data in the problem description without generating a plot, PLT-NO should be entered.

PLT- can also be entered in the parameter data, Sect. Fil.4.3, but will be over-ridden by the value entered here unless the problem is being restarted.

Fil.4.12 REFERENCE

l. N. M. Greene et al., AMPX: A Afodular Code System for Generating Coupled Multigroup Neutron-Gamma Libraries from ENDF/B, ORNL/TM-3706 (March 1976). Also see Sect. F2.3.8 of the SCALE manual. ,

2. J. R. Knight and L. M . Petrie, 16 and 123 Group Weighting Functions for KENO, ORNL/TM-4660 (1975).

i-l l

l'

. F11 A.42 1

Tables summarizing KENO V input data follow, i

. 1 1

l l

i i

Table Fil.4.7. Summary of parameter data TITLE The title must be entered first ISO colemasi see section F11.4.3 FARAMETEDS Formate BRAD FADAM enter parameter dets here' END FAB AJS If parameters are entered, they must follow the title. See Sections F11.4.3, F11.5.2 and F11.5.3.

ERY 'STD. DEFINITION REY STD. DEFINITION REY STD. DEFINITION FRY STD. DEFINITION RND* given sendem aanber RUM = YES esecute problem MRH= No maEris by hole asc- in mis.d ssoc.

TNR= 30.mia esecution timetmial FL2= NO fluses CRn= NO cofactor k by hole ALn= 73 albedo TBA= . 0.5mia ' bat ch t ime smial FDN* NO fissica densities FMNa NO fiss. prod. by hole NT5 4 8 0 weights NTAs 0.5 everage weight ADJ= No adjolat calculation NNL= NO MRE et highest level LID = 0 working rsees .

NTM= _3 . 0 wt. for splitting AMK= NO sit masture asoce MRA= NO matris by array SET = 16 scratch

]

NTL= fiNTN mussten poulette vt. KAF= No swee angles a probs. cKA. NO cofactor k by array asT= 0 reed restart  :

A  !

GEN = 103 No. of generatione 251= NO 1-D ssees FMA= NO fiss. prob. by array was. 0 write restert g NPG= 300 No.' per generation RS2= NO 2-D ssees MAL =.NO MKA at higest level NSF= 3 generations skipped PRI. NO fissloa spectrum PLT = YR$ printer plots tracks Res.' O gens. between restert F1D= NO outra 1-D asses BUG. NO debug praat NBR= GEN *25 neutron bank positions' 'FAR= MO fiss 6 abs. TRK. NO print neutron treeks r

INB= 0 estra bank entries . WrF= No metria by location twt = NO print avg. weight NFBs NPG fissica bank positions CEF= WO cofactor k by loc. PGM. NO saprocessed geometry XFB= 0 estra beak entries FMP= No fiss. prod. by loc. 3 mum NO self-multiplication 11D= 0 No. of astra 1-D's MEUs NO matris by unit' NUB = NO neutrons per fission LNG = 4000000 words of storage cze. No cofactor A by unit FAX = NO elbedo-esec-array SEG= 1 restart at this gem. FMU. No fiss. prod. by wait Ne8 200 blocks for d.a. unit.

~

NLS= 789 ' leagt h of d.a. block

_e- _m_ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ . . _ _ - --__m---- - - - - _ _ - - _ _ .

Table Fil A.8. Summary of array data A9 SAT Formats DEAD APRAY array parameters date t ype orientation date .END ARRAT s...s.ctions Fei.s.s. ris.s.e and ris.s.1 Re pe a t the sequence ARRAY FARAMRTERS DATA TYFR ORIENTATION DATA for each errey used la the problem.

ADRAY FARAMETRR$ DATA TYFR RETWORD DEFAULT DEFSN1 TION PALL LDOF

~' ARA = 1 No. defining the ersey NUKE i No. of units in I direction NUYe 1 'No. Of units la Y directica

' nut = 1 No..of units la 3 direction GPL= masers The global, universe or overall errey numberee COM. mene dette comment delin optional comment is a mesimum of 132 cherectors, se Can be defaulted by the code. If specified.

it need be entered only once per problem.

ORIENTATICM DATA FOR F1LL CRIENTATION DATA FOR LOOP Bater unit numbers to define every posittom in the errey. Enter the unit number -and aime .aumbers that define the when entering dets utilizing the options in this table. the count positionist of that unit. Data for each of these ten entries field and option field must te adjacoat with no sabedded bleaks. are repeated until every position in the array has been defined.

The operand field may be separated from the option field by one or Data for en array is terminated by materlag END LDOF. ag l "

more bleaks. F111 date for en array ends with twD FILL. .==

ENTER DATA IN THE FCSM L ""

h Es C004T OFTION OPE 9AND DATA F1 ELD F15LD FIELD . COMMENTS ENTRY COMMENTS j stores j at the current positaos in the array LTYFS The unit or bos type. LTYPE must be greater than 8.

1 3 j . stores j 1a the most 1 positions la the array' IX1' Starting position la the X direction. 121 must be'at:

1

• j stores j to the most i positions in the errey least 1 and no larger then the welue entered for NUK; i 8 -3 stores j ta the most i positions la the array 112 Ending positaos la the X direction. 122 must be F j fills rematador of the errey with east No. 3 et toest 9 and no larger than the value of NUE.

starting with the current errey position INCE The number of unite by,which tacremente are

.A j sets the curreat' position la the array to j mede in the X directice. . .

1 5 lacraments current position la the array by i ITt The starting position in the Y direction. 111 must be ellows skipping i positions. The value of 1 . et least 1 and less them the value estored for NUY.

.may be positive or sogative. 1Y2 Reding position la the Y directica. 1Y2 must be i Q. j repeats the prewtous j ostries i times. The_ et least 1 and me larger then the value of NUT.

default welue of 1 is 1 INCY The number of units by which tacrements are made i N j repeats the preslons j entries i times. la the positive-Y direction.

lasettlag the sogmeare each time. The default' 151 $terting position in the E direction. 1R9 must bei welus of 1 is 1. at least 1 and no larger then Nut.

I R ' .) Starttag with the entry at -1 from the current . in the positive Y direction.

position, store entries la inverse order entti 122 andtag position la the E direction. 112 must be-position .ti+ji is resebed. Default value of 1 1. et least i and to larger than NUE.

i F j. alternately stores j and -j in the meat 1. INCE The aanber of units by which increments are sede positions of the array. . in the posittwo E direction.

1- 1 3 k provides i entries 11mearly interpolated between j and k..the sad points ti.e. e

' total of $+2 potate.5 j and k must be separated by et least one bleak.

T terminates the data reading for tha array.

• +

~ , __.a. - _ . ~ _.,. - - . - - . - , u. , . . ~ . , -

Table Fil.4.9. Summary of biasing data BIAS Formats BRAD BIAS keyword correlation date aus111ery SND FIAS tweightingi See sections F11.4.7 and F11.5.9 ,

REYvoso cesCp!PTIDM MATERIAL ID ENEDGY GDOUPS TWICKNR$$/INCptMENT ID* CoaRELATION DATA will be reed most. concrete 301 16, 2?, 12) 5 cm 16 material ID. Enter from tehle et right. pereffte 400 16, 27 123 3 cm to use weighting date from the library. water 500 16, 27, 123, 218 3 cm ibga beginalag bles ID graphite $100 16, 27 123 20 cm iond ending bias ID WT= AUXILIARY DATA will be read aest.

WTS= AUXILIARY DATA will be read nest.

wttiti meterial title id meterial ID. ~

asets number of sets of group structures q EftRAT TNK!WC, NUMIWC, NGPWT, WTAVG NSRTS TIMR$

thkine thickness per increment- ."

ausiac number of lacrements agput number of energy groups for this set of wts .N utavg enter annines agpet values 6f wtevg.

For CORRELATION DATA, the Meterial ID is chosen from material ID ect.ma .bove othe m.yword 1. :D. .

For AUXILIARY DATA, the material 10 is chosen by the meer and the keyword is WT= or WTS=.

Beginalag and ending bias ID's ese defined by the user. The geometry speelfication that has the bles 3D equel to the begl'.!ag bias ID utilises the et avg's from the first laterval of meteriet ID.

i t

s

e Table Fi1.4.10. Summary of boundary condition data

'BNDS Formats READ SNDS ~ face code albedo name RWD BFDS selbedo or See section F11,4.f I boundary condittoast The sequence FACE CODE - ALSEDO MAME le entered as many times as necessary to define the appropriate albedo boundary conditions. The defecit for.all faces is veenas.

FACE CODES FOR ENTERING BOUNDART tALBEDOR CONDITIONS 5 b

FACE ' FACE PACE FACE DEFINITION CODS DSFINITION CODE . DEFINITION CODE DEFINITION i

CODE .. \

i positive I face IFC= t,oth X faces +YEe positive I and Y faces EIT=. positive Y and E faces

- +Re=. -KY= negative X and;Y feces ars= poestive x face 'YFC= both Y faces $2Y. positive X and Y faces negative I face .EFC= both E faces S TE= . positive X and Y faces -IE= negative I and E faces-

-28=

+FC. ell positive faces +1Em positive X and E faces -YEe nogetive Y and E facee ,

4TB= positive Y face SYS= positive Y face SPCs all positive faces +EE= positivs I and I faces YXFe all X and Y faces negative Y face -FC= all negative faces $11e ' positive X and 5 faces EXFS all 1 and E faces

-YB=

XYF= ~ ell X and Y faces 65X= positive X and E faces ETF= all Y and E faces

• E9=. positive E face SES= . positive E.fece XEF= all K and E faces +YEe positive Y and I faces -TX= megative X and Y faces negative E face 'YEF= ell Y and E faces +EY= positive Y and E faces -II= negative X and E faces , ,

p

.-58

• If= positive 1 and Y faces . SYse positive Y and E faces -ITe nogetive Y and E faces.

'ALL= .all 6 faces

.'U i 4

l"*

' A

\ 'k  !

- C

ALBEDO NAMES AVAILABLE ON THE ERNO V AL9tDO LI5pARY. FOR USE WITN TER FACE CODES sr

. i ALBEDO: ALBEDO ALDEDO MAME DESCRIPTION NAME DESCRIFTION NAME DESCRIPTION.

s 12 fach double FO water CONC-4 4 Sach concrete differentist VACUUM veceum condition

' DFON2O

. differential albedo with CON 4 albedo with 4 incident WOID DFON2O

4. incident engtes CONC 4- eagles TACU DF0 VAC DFO [

CONC.9 9 tach concrete differentist .

SPECULAR .eltror Amege reflection

,? _N2O .

12 inch water differential CONS elbedo with 4 tacident MIRROR 4

NATER albedo with.4 incident CONCS eagles MIpW eagles SPEC 2

12 inch paraffin differen . CONC-12 12 inch concrete differential SFR FARAFFIN tial albedo with 4 lacident CON 12 albedo with 4 incident MIR f FARA

WAX angles, . ..

CONC 12 ' eagles PERIODIC . periodic boundary condition 9 CARBON 200 cm. carbon differential CONC-16 16 inch concrete differentist

'FERI CRAFNITS: albedo with' 4 incident angles CON 16 albedo with 4 lacident CONC 16 . eagles FER C

j .

12 lach poly 9thylene. CONC-24 24 inch concrete differential 3

.31NYLENE FOLY differential albedo with. CON 2e elbedo with 4 lacident ,

a ,

s 4 incident angles CONC 24 angles

.CH2 i

4 3

i-

+

ei .d

, up- -'

t.g T' s w .4 -ne'

Table Fil.4.!!. Summary of geometry data CEOMETer rormat, MEAD cEcM .ater ...m.try r.asom date h.r. Ewa GEo-er.,som> S.. S.ctions ris. ... rii.s.i.3, ris.s.. .ad ris.s.Y CEOMETRY ptGION DATA coaststs of SIMPLE CBCMETpf SEGION DATA and EXTENDED GEOMETRY REGICM DATA.

ENTER CROMETRY BEG 10W DATA IN THE FOLLOWING FORMS OPTIONAL CLOBAL SPECIPICATION UNIT a CPTIONAL GEOMETRY COMMFWT

$1MFLE CEOMETRY PEGION DATA and/or IITENDED CROMETRY REGION DATA e e e e e o e e e o e e e e o e o e e e e e o e e o e e ENTER SIMPLE CEOMETRY RECION DATA IN THE POLLowInc PosM GLOBAL Enter only to specify this unit as the global matt.

UNIT a COMadelle comment dette This optional erament can be up to $32 characters.

It most begin and and with a de11etter.

fgeon mis no. bias ID dimenssoas optional ortgta data scSICM coordinates: Optional chord data (CMORDI Enter as meny geometry description specifications as necessary to describe the unit and as many 'T!

=

units as necessary to describe the system. P A

TYPE OF TYPE 1 SIMPLE CEOMETay mEGION INFUT DATA SEQUIREMENTS TYPE 2 TYFE $ TYPE 4 TYFE 5 TYPE 6 h

DATA DATA DATA DATA DATA DATA DATA fgeon SPEEEE RCYLINDER TCYLINDER CYLINDER CUse CUSOID NEMISFREBE IREMICYL+T YREMICYL+1 BCTLINDER REMISFREFE*1 XREMICYL-Y YN EMICY L-X EMEMICTL4R REMISFRE9E-X KNEMICYL42 YWEMICYL*$ $NEMICTL-R REMISPRESE+T 2REMICYL-E TREMICYL-2 SNEMICTL+T BEMISPREEE-Y 2REMICTL-Y REMISFREDE*S NEMISPEERE-E dimensions a tradiest B 4R -W R .R -R p *R -n .x -E 4 3 -x .T -Y *1 -t optional Enter,the Enter the Enter the Enter the omit omit origin X YI coord. TE coord. I I coord. 2 Y coord.

coord. of origin of center- of conter- of center-line line itee optional Enter the Ent e r t he Reter the Enter the ' omit omit chord dist. to dist. to $1st. to dist. to datee* plane plane plane plane

• • Chord data is not applicable for EPWEDE 1 CYLINDER YCYLINDER CYLINDER or ICYLINDER ,

Table Fil.4.ll (continued)

CEOMETST ENTER EXTENDED GEOMETRT DATA IN THE FOLLOMINC FOPM:

Iregicas teost.I fgeon ref. ID bias ID thickness per regica origin ceerdtaates preg EXTENDED GEOMETRY BEGION INPtf7 DATA REQUtaEMENTS

. TYPE OF TTFE 1 ' TYPE 2 TYFE 3 DATA DATA DATA DATA fgeoe ARRAY MOLE BEPLICATE COPE DFFLECTOR COREBDT CORESNDS CostsOUN .

ref.'1D errey no. emplaced etztere me.

seit in generated 7" assber regions  %

1. s oc bias ID omit for ARRAT omit first bles ID tbsek. frog. omit omit variebie**

origin Eater the Enter the cait coord. I T E coord. X Y E coord.

of most meg. of origia pt. of array areg omit omit No. of regions to be genereted i

• • The number of dimenstoms to be entered is the some as the region preceding the replicate or reflector specificettoa

• because tbs generated regions have that shape. The veine of the dimensions is the thickness of each genereted region of material on that surface.

E

. 1 t-

Table F11.4.12. Summary of mixing table data I

l MIXTUsES Format SEAD MIET asse parameters mistag table END MINT This date is entered only if en AMPI working formet library is beleg esed, (Lis=$ in the parameter date. Do not ester if an ICE sized library is used, 825C=a la the parameter data.

See Sections F11.8.10 and Ft1.5.5 X$EC FAPAMETESS consists of keywords and assoeleted values.

These persseters. af estered, need be entered only once.

FEYWORD DEFAULT DEPINITICW 5CT- 1 No of daserete scattering angles.

0 1s isotropte 1 is F1 2 is P3 )

3 is F5 y

Er$= .000D3 Cross section message cutof f walwe. A A

Use to suppress message No. K5-69 4 MII1pG TABLE DATA consists of til e keyeard and misture ID for the misture The keyword is MfI=

The desired as sture number f ollows t he keyeard.

I2a acetide 1D**

138 member density **

• • the sequence 42s t3e se repeated for each auc!!de in the an sture.

PEPEAT the sequence 417 f21*s f31's unt 1 ell the mistures bawe been described.

~

5 ,

9 "[ 3(3D C

~

~

2 e 2M e .

t g g 2 o a e n t e e l t pg d i t 1 L a.

e e e e po n k u 2 a

h t

h t

h t

h t

r h

t r

h t

r sps o

l sp ong d e

a c h

e o

h t

0K 2

e.

s r r r c e o o o o o srwa socop n

a e e i

w 9J 9

3 -

f f f f f f t ad r t ad 1' ep e e e e se eeg ot e a 5 e e e i tddht a cas 8I 3 s 5 e) et ne s a ed t

a 1 t s t s t s l t t caeet cl aa 7 7 /

s s ss ss et sl st pt tt s e d oo oo oa oacwom ce- onasr n erb 7 H 3 . 5 cr cr oo cr c cv o o e npiiwai e rr eh g ot o o e t 1 6 6 4 c c 4G 4 1 ns ne me sd md nd e n p pd c e we bg

.tf t e

l p

oe ot ot eE t

oa oi i t eeed e nm t 1

5 $ e s s t i

$F $

t t tt tt t t tt tt ewbbeneieme e 3 co co eo co e o co bt t ohrl et h 1 el el el rp el r p el rp el r p eoon gbtti a t t bl t sobo t

4 E 4 ,

3 4 e 5

r p r p s g i i e r rol 1 i

d e de i i de i

d e de de l gsspel rpr p a w. 3 x 3 3 h h h h h h enl l t ae p t e 3 D 3 5 f t f t f t f t f t ea aaht nt e e d . l 1 f t o pcv vcegch sh et e 2- 2 -

o o o o o f s er ra4iat ot eo b 2C 3 $

f f f f f t o t o t o t o t o t o pees sr t rl 1 s n n l st t ' S ases p a 1 v 1

• M n n m a osrR rh wnu s e 1 9 3 5 C es es es es es es we w 1 nt nk nt et nt mi tl n1 eE ecoa o 0v I

T oa os oa cn oa es na pct l mi e 3g 0*

pe pa pe pa pe pe ocf f i el rt l g t A 3 1 I l e N m m m m m m sioosash eee e i

9r t t I ox oX oX oM oW aW it

.nl1 el 1 t S

t 3

et k r 99 2 a F cA cA cA cD cD t D r t .

oeooieef FO8 Oa a E

E h wnnldd oYN7 Nm 88 0s s -

C I T 3 I Y a t

a $

B 1 7 2

a N 7 . 7 a

d C 66 2 t md Rd pd 9s Rd Rd f SS 6c 6 s o t o

catOat eo eo catCatCat eo eoC. eo e' o 2 e lp '4 4 lpA XrlpARrl pA 2 rl PD M rl pDWrl pP Wr s 5 F 5 r T Us e 3 3 2 4 f

o L U

A

. W to vF

.Ds .cs vF i

vP i . vFF s .wFUs i i vF a

S l m

22 4 o 4 >

y R S S e 2 4 r F E

oI r

2 oI A2r oI A XeI A r r WeI MDroI wD Dr N E E w 1 1 a 9C Y T 3 = 3 4 R p0W p8W p0V p8wpSW p0v t 6 2 4 m l u A A A m D. a 'I $ I = I S u 9 . f DR D= DR C . *

• a * * * . e EW E= EN S w - * =

• W u

=

W 2DAWI E u T d MC RC MC T 2 2 J D C LLADPC e L *

. r A A 4 C 3 t U V W C T # DDMNLN t T

• 1 A

1 1

e d ttt F a ttt eoo m oool ll le e r

ed' l l l ppg ppp y .

b b t n .

fff ai e a ca O . fff ooo r h T o a rg NO N ooo rrr r r. t t ar .

aa T rrr eee y r f y s ht I 5 eeennn r ee oer i cn N1 nnnrr r t h a U r r rooa e t1 ar S

t a

el ng .A E S

ooocce ccc m

o f h l a g

oeb E t P h . RI eES 5 P Y D- T ttt e g

ool t l ra t T T I R ttthhh A l V U A t g ob TT SS CC S f f f ggg to ol t

h t

e t Tr i K o tI T2XXrD A1 I I rE TTt I 0O0wu1 TT 1 I rt! 1 FAAs! ! TT M1 ! Tt ECG I$OwuW ww eeeiii lll rrr f

o la.

eh el hg o

L p M MMMMMM 9D9rtU rrrrrr e pt t P es s l eo:

.t

- - - eeeeee pppwww t

hh e

h - g ' of Dc l al l e - -

- pppooo i wo tt wa ent pr u

- uuelll r t i te d gi -

~

o t r wf i t et ~

- . f ff ff f a. o r is h c -

O oooooo h g. s eo W t et i p

W t o. en rf 9 D t rh E .

i so do e I t et s O D dddddd w c ii td5 T pt i f R r rr r rr t ct ee I l f o U W I oooooo s s= op mr1 N eaot T oooooo e oc st S

a e1 rt F I st Fl lda p t e I I

T I A cccccc d i

me s ce s or aa T eent y M W I 2YI KTE c- e ped D dd apt F B n . e n i h d.

t Yd t ea o a A l

ob pt1 1 c'.

Tn th a -

t st sA AR tttttt s oooooo I o 3 tu8 l l l l l l Ni 7 A r. DA om.

L 1 T ppPppp Ut p Ri a

E Tr Et mr Co P s1 De rF L E , e A bl wvvvwv.

eooooo r Lr Ce t e t tt At s P ot T rr rr r r a Ms n fs ren E ri A ppppppl 1 e Ai EO aso ai D pt R _C I

$d Bi SC 9 1 D 5 i ec rt D a t C 1 2 3 t pe R ( E f a S O L C s i * * . . T mt W T I LLLApSO roe YT P UUULLLL ol e E NYSErSP F pS R T

O L

r a !j > '

Table Fil.4.14. Summary of starting data START Formate READ STADT enter start data here END START The default vales of start type is sero.

See Section F11.4.9 START ptGUIRED OPTICNAL STARTING TYPE START REOUIRED OPTIONAL STARTING DATA DATA DISTRIBUTION TYPS DATA DATA DISTRIBUTION FRYwonO DEFAULT DEFINITION 0 none NST unsform J NST srs spike NST= 0 start type MSM TFX PSP TFx. 0.0 X coordinate ESP TTY TFYa C.0 Y coordinate TSM TFE TFS= 0.0 $ coordinato 1SP NES NXS= 0 R lades of unit pos.

ISH NYS NYS= 0 Y indes of unit pos.

• ESP NSS NES. 0 3 indeu of unit pos.

DFL PSP FFS- fAssion spectre 3 4 NST RFS multiple Lwu. O member of last asutroa 's ,

TFR PSP spiD es NBN. O TFY source unit number b FCT= 0 fraction ""

i NST ISM cosine TFS XSM. -X -1 of source cuboid

' ISP M82 ISP* +X *M of source cubold YSM YSM* -Y -Y of source cubold TSP' YSP= +Y +T of source cuboid SSM 5 NST PSP in specified ESM= -r -8 of source embold 159 NBR unita ESP. +3

• E of source cuboid, RFL PFL. NO start in reflector PSP G NST NIS arbitrary PS6e NO print start 6 impet TPE NYS points PSP = MO 2 NST XSM cosine with print starting potats TFY NES NXS 13P fraetto. i. Tr8 ars NYS YSM specified LNU* PS6 Nf3 TSP unit PSP r

FCT SSM SSP RFL PSP

• LaPJ must be the last entry for each set of start 6 data. The LNU of each successive set of date must be larger than the last.

b, ._ _. .m -.. _ . _ _ , _-- _

.w,-_. . -. . . . . _-

, m,,.m._ ...m. ._mm = __--,_m= _ ._.=.m__- . _ _ __ --._=__5

au , .- -- - -..a >+4.- 2.- a s .2 . ass--,, .. - , > .>e-..-- i..- a.-.--am-, r .a a . s-.. - - ..-ssa.--wt, + a.aw+.,~--.as-6 >~ - ~ , _ -. -

r h

i f

5 1

k i

f 6 i

4 I

i' e

f I

i k

B k

b

+

l m

.E e

t b

i 1

F 4

9 i

k I

s t

5 I

r Y

t J

n i

+

) ,..

q w y. i p.r-9 fiY f 'N ""Tg .+i+ y.,p,a g. ,.

p ,

- -,- ew ..,,..4 m. ._v.,,.,,,,m__ , ,_ _ , , .g,, __.,, . , , .. ._ ,, , , ,,.

I Fil.5 NOTES l'DR KENO V USERS j

. This section provides assorted tips primarily designed to assist the KENO V user with problem  :

mo(k.ups. Some information concerning m thods utilised by KENO V is also included.

l'11.$.1 DATA ENTHY f The KENO V data input is entered in blocks that begin and end with keywords as described in Sect. 111.4.1. Only one set of parameter data can be entered for a problem llowever, for other data blocks, it is possible to enter more than one block of the same kind of data. When this is done, only the last block of that kind of data is retained for use by the problem.

Within data blocks, a number, t, can be repeated n times by specifying nRx. n't. or n$x.

YlI 5.1 I Multiple am,' Scattered Entries in the Mt.rtng Table in the following examples, assume 1001 is the nuclide ID for hydrogen. 8016 is the nuclide ID for ,

ox)ren,92235 is the nuclide ID for 2 "U. and 92238 is the nuclide If, for 2 "U. If a given nuclide ID is used more than once in the same mixture, the result is the summing of all the number densities associ.

ated with that nuclide. For example:

MIX I 92235 4.3 2 92238 2.6 3 1001 3.7 2 92235 1.1 3 8016 1.8 2 would be the same as entering:

MIX.192235 4.412 92238 2.6 3 1001 3.7 2 8016 1.8 2 A belated entry for a mixture can be made as follows:

MIX-l 1001 6.6 2 MIX-2 92235 4.3 2 92238 2.6 3 MIX-18016 3.3 2 This is the same as entering:

MIX-1 1001 6.6 2 8016 3.3 2 MIX.2 92235 4.3 2 92238 2,6 3 Fi1.5.I.2 Multiple Entries in Geometry Data Individual geometry regions cannot be replaced by adding an additional description. flowever, entire unit or box type descrip: ions can be replaced by adding a new description having the same unit number. The last description entered for a unit is used in the calculation. For example:

READ GEOM UNIT I SPilERE I I 5.0 CUBE O I 10.0 -10.0 UNIT 2 CYLINDER I i 2.0 5.0 -$.0 CUBE O I 10.0.!0.0 UNIT I CUBOID 111.0 -1.5 2.5 -2.0 3.0 -6.0 CUBE O 110.0 10.0 END GEOM is the same as entering:

Fi l.5.1 i

I

-~.r- . -,, ... . - _ _ . - . . _ - - i,--.--- n.-.-,r ,,, ..-.r -.. - .., ,-c, . ~ . . _ . . , , - , , . , . - - . - _ . , - , , . . . w -, _m., --.... . - - , 7

- . - . . . . - ~ - ._- .

Fi l.5.2 RI'AU GEGhl UNIT 1 CUB 0lD 111.0.l.5 2.5 2.0 3.0 6.0 CUBE O I 10.0 10.0 UNIT 2 CYLINDER I I 2.0 5.0.$.0 CUBE O I 10.0 10.0 END GE0h!

ot.

READ GE0h! UNIT 2 CYLINDER I I 2.0 5.0.$.0 CUBE O ! 10.0 10.0 UNIT l CUBolu I I 1.0.l.$ 2.5 2.0 $.0 -6.0 CURE O 110.0 10.0 END GE0Al The order of entry for unit or bos type descriptions is not important because the unit numbe is assigned as the value following the word UNIT. They need not be entered sequential!y nor he num.

bered sequentially, it is perfectly acceptable to input Units 2,3, and 5, omitting Units I and 4 as long as Units I and 4 are not referenced in the problem. It is also acceptable to scramble the order of entry as in entering Units 3,2, and 5.

Fil.5.2 DEFAULT LOGICAL UNIT NUMilERS FOR KENO Y The logical unit numbers for data utilized by KENO V are listed in Table Fil.5.1.

l Table Fil.5.1. KENO V logical unit numbers i

Parameter Unit Variable Function Name No. Name Card input Data 5 INPT l Program Output 6 OUTPT l Albedo Data ALB - 79 ALBDO Scratch Unit SKT- 46 SKRT Read Restart Data RST= 0' RSTRT 346 RSTRT l Write Restart Data WRS - O' WSTRT i

35' WSTRT Direct Access Storage for loput Data 8 DIRECT (1)

Direct Access Storage for Supergrouped Data 9 DIRECT (2)

Direct Access Storage for Cross Section Mixing 10- DIRECT (3)

Mixed Cross Section Data Set XSC - 14d ICEXS Group Dependent Weights WTS - 80 WTS AMPX Working Format Cross Sections- LIB - 0' AMPXS l

' defaulted to zero

• defaulted to 34 if BEG- a number greater than I and RSTRT-0

' defaulted to 35 if RES- a number greater than rero and WSTRT-0 l #defaulted to 0; if LIB. a number greater than zero, ICEXS is defaulted to 14 i:

1 i

Fil.5.3 Fil.5.3 PARAMETER INPUT When the parameter data block is input for a problem, the same keyword may be entered several times. The last value that is entered is used in the problem. Data may be entered as follows:

READ PARA Af FLX= YES NGP 1000 TAfE-0.5 TAfE-I.0 NPG 50 ThlE-10.0 FLX-NO NPG- SUU ENDPAK4 This will result in the problem having FLX-NO, TME.10.0, and NPG-500. It may be more conven-ient for the user to insert a new value than to change the existing data.

Certain parameter default values should not be overridden unless the user has a sery good reason to do so. These parameters are (1) XID which defines the number of extra 1 D cross sections. The use of ext.a 1-D cross sections - other than the use of the fission cross section for calculating the average number of neutrons per fission - requires programming changes to the code;(2) NFB- which defines the number of neutrons that can be entered in the fission bank;(3) XFB which defines the number of extra positions in the fission bank (the fission bank is where the information related to a fission is stored); (4) NBK- which defines the number of neutrons that can be entered in the neutron bank; (5)

XNB- which defines the number of extra positions in the neutron bank (the neutron bank contains information about each history); (6) WTil- which defines the factor that determines when Russian roulette is played;(7) WTA which defines the default average weight given to a neutron that survives Russian roulette; (8) WTL- which defines the weight at which Russian roulette is played; and (9)

LNO- which sets the maximum words of storage available to the program. It is recommended that ilUG , the flag for printing debug information, never be set to YES. The user would have to look at the FORTRAN coding to determine what information is printed. BUG-YES prints massive amounts of sparsely labeled information. The user should only rarely consider using TRK-YES. This generates thousands of lines of well-labeled print that provides information about each history at key locations during the tracking procedure. All other parameters can be changed at will to provide features the user wishes to activate.

Fl1.5.4 CROSS SECrl0NS KENO V always uses cross sections from a mixed cross-section data file. The format of this file is the Monte Carlo proces'.ed cross-section file from ICE-II or ICE S (Sect. F8). A mixed cross section file can be created by 1) executing ICE, or (2) by using an AMPX working format library and enter-ing mixing table data .n KENO V.

Fi1.5.4.1 U.se a ;en :xed Cross Section Data File A premixed cros. stion data file from ICE or a previous KENO V case may be used. This file should be specified in the job control language on the unit number associated with the parameter XSC . When a mixing table data block is entered, the premixed cross-section data file will be rewrit-ten. Therefore, a mixing table should not be entered if a premixed cross section data file is used. The user should verify that the mixtures created by ICE or the previous v 0 V case are consistent with those used in the geometry data of the problem.

l

F11.5.4 Fl1.5.4.2 Use an AAfrX Working Librar;*

When an Ah1PX working library is used, a file definition card must be used in the job control lan.

guage to specify the AMPX working library on the unit associated with the parameter LIB., if the . ,

mixed cross-section data file is to be saved, a file definition card must be used in the job control lan.

guaFe to specify the mixed cross section file on the unit associated with the parameter XSC .

I Mixing table data must always be entered when an AMPX working library is used. ID's used in the mixing table rnust match the ID's on the AMPX working library.

Fl1,5.43 Number of Scarrering Angles

'Ihe number of scattering angles is defaulted to one. This default is not edequate for many upplica-tions. The user should specify the scattering angic to be consistent with the cross sections being used.

The number of scattering angles is entered in the cross section rnixing table by using the keyword SCT . See Sect, Fil.4.10.

The order of the last Legendre coefficient to be preserved in the scattering distribution is equal to (2xSCT 1). SCT-1 ould be used with a P, cross section set such a's the 16. group linnsen Roach cross-section library, and SCT-2, for a P cross-section 3 set such as the SCALE 27 group cross section library. Isotropic scattering is achieved by entering SCT-0.

F1l.5.4.4 Cross Section Alessage Curoff The cross section message cutoff value, pbxs, is defaulted to 3x10-8 Warning messages that are generated when errors are encountered in the Pt expansion of the group to-group transfers will be suppressed if the Po cross section for that particular energy transfer is less than pbxs. The value of pbxs is specined in the cross-section mixing table by using the keyword EPS=. See Sect. Fl1.4.10.

The default value of pbxs is sufficient to assure that warning messages will not be pdnted for most of the SCALE P iand P cross section libraries. Ilowever, the 123 GROUPGMTil library requires a 3

value of pbxs as large as lx10-8 if P cross 3 sections are specified.

If the default value of pbxs allows too many warning messages to be printed, a value can be deter-mined from the printed messages by choosing a number larger than the Po component on the first line as shown below.

Tile LEGENDRE EXPANSION OF Tile CROSS SECTION (PO-PN) IS (Po) (P i ) (P3 ) .

(P.)

Tile MOMENTS CORRESPONDING TO Tills DISTRIBUTION ARE

( Afi ) ( Aft ) . . .

(Af.)

THE MOMENTS CORRESPONDING TO THE GENERATED DISTRIBUTION ARE

( Afi ) ( Af ) . . . (AI.)

Tile LEGENDRE EXPANSION CORRESPONDING TO TilESE MOMENTS IS (Po) (Pi ) (P3) ... (P.)

MOMENTS WERE ACCEPTED r.- = .-- , - - - , , , ..y, ,,,,,,,-o,,y-,,y --.-,--,y.,

, , , , , , , y , - ,,, ,, m.,,,,-y-- , , , , ~ . - -3 _ ., ~-<y,-

F11.5.$  !

I for the following messages EPS=7.5-4 would cause all three messages to be suppressed. A valu'e le than 7.295643-4 and greater than 5.662553 4 would suppress the last two messages, and a value less than 5.662553-4 and greater than 4.398203-4 would suppress only the last message.

i 8540 THE ANGUL AD RATTitlNO DIST*l8UTION tot MIRTUtt 2 H AS D AD MOWLNis FOk 1Hf TR AN5 Fit rkOM OROUP 4 TO GkOO )2 2 MOMENTS D e #1 AtttF1LD THE L1GENDP1 E KP ANSION Of THL t RCES stCT1oN IPSPNI15 1794416.4 4 ? sus 4t49 3 $4Il0$f M 3 5307t0144 THE MOMINn COPR15PONDING TO THIS DistRIBUTSON ARL e %MM1b42 9 httt4M1 -9 9;sueSM2 THt' MOMt NTE Co#R1%PONDlNo to THf oLNt A4'T D DisitipOTION Akt 6 $MMID02 9 48864fAO) -4 Tilf t0t4d THL L EGI ND#l L AP ANSION (OR RIAM)NtilNO TO THIAL MOML NH 15 179 4416 64 4 7tue4tE05 4 $4110st4d .? toltMMn Me 1Hf ANGULAk M ATTE plNO (stSTRittrf joN )OR MigTUp! 2 H AS $4D MOMINTS FD) THE Tet AN$f it ikOM 0kOUP 410 0kC UP H

• 2 MOMINTS u t Rt ACCEPitD THf LIGI NDR E l AP ANMON Of THE ( ROS5 blCTION (P4PNill  ;

1 M2151104 31stt24E41 214tt28E M .I 476078144 T Hi MOMt NTS (OR R LAPONDINO TO THIS DIS 1119UllON AD E

% trm?voM2 ? 4ett47t:41.I be tte9Mi THE MOMI NM cop plAPONtalNG 10 THE 01Nik 4Tl b T 'T 'f ' iN A * *

$5R190tA02 1 4914411:4 1 41426414d 1Hf LIGI Nt'k! (XP AN% ION cop klSPONDING TO Tha ' *M is \

S H23911.44 3 20st24Mi 2167628tud -e l191Eb43 M 46 THf ANGUL AR bCATTIPING Dl5TR18tft10N FOR MIXTURE 26 5 .? , $ 4 rCa -a 3811R ANsfit rkOM 090VP 4 To okOUP Si 2 MOMt NT3 WI RE ACC LPTf D Tht LIGLNDRE LAP AN$10N OF THf CRO$s stCTION (PD PN)is 419620)t M 2 2610$)t45 214s241L44 154H7214

, THE MOMENn(DRkEAPONDING TO THIS blifit9UTION Akt

) 640teoM2 $ tuud6tLol .109W10$ Del THE WOMt Nis CD8PIAPONDING To THE of NLRATID Dl5TRf 9VTloN ARI 1140se0M2 $ 6Mrd4D4J 4 MilllD44 THE LIGE NDRI ( APAN$10N (t)$ $ t3PONDlNO TO THtal MOMEN1118 4 Jvt2U1E44 2161015D43 2 IMu411Md .3 340110tLOS The user need not attempt to suppress all the K5 60 messages. They are printed to inform the user of the fact that the moments of the angular distribution are not moments of a valid probability distribu.

tion. The fourth and fifth lino of the menage list the original P,, components and their moments. The sixth and seventh lines list the new correct:d moments and their corresponding P,, components.

For most criticality problems, the first moment contributions are much more significant than the contributions of the higher order moments. Thus, the higher order moments may not affect the results siFnificantly. The user can look at the original moments and corrected moments and make a judgment as to the significance of the change in the moments. .

F11.5.5 MIXING TAlllI Mixtures can be utilized in defining other mixtures. When defining mixture numbers, care should be taken to avoid using a mixture number that is identical to a nuclide ID number if the mixture is to be used in defining another mixture. If a mixture number is defined more than once, it results in a summing effect.

The nuclide mixing loop is done before the mixture mixing loop which mixes in the order of data entry. Thus, the order of mixing mixtures into other mixtures is important because a mixture must be defined before it is used in another mixture. Some examples of correct and incorrect mixing are shown below, using 1001 as the nuclide ID for. hydrogen, 8016 as the nuclide.!D for oxygen,92235 as the -

nuclide ID for 2nU, and 92238 as the nucl.de ID for 2nU.

- - - - - - -. .- - . - - - - - - _ ~ . . - - -..-.-.-- - - -

r Fl 1.5.6 4 EXAMPEES OF CORRECT USAGE (1) READ MIXT MIX 1 1001 6.6 2 8016 3.3 2 MIX-210.5 END MIXT This results in mixture I being full density water and mixture 2 being half density water.

(2) HEAD MIXT MIX l 2 0.5 MIX-3 1 0.5 MIX 2 1001 6.6 2 8016 3.3 2 END MIXT This results in rnitture i being half density water, mixture 2 being full density water, and mixture 3 being quarter density water. Because the nuclide mixing Imp is done first, mixture 2 is created first and is available to create mixture 1, which is then available to create rnisture 3.

(3) READ MIXT MIX 1 10016.6 2 8016 33 2 MIX 2 92235 7.5 4 92238 2.3 2 8016 '

4.6 2 I .01 END MIXT This results in mixture I being full density water and mixture 2 being uranium oxide containing 0.01 density water.

(4) READ MIXT MIX 1 10016.6 2 8016 3J 2 MIX-2 92235 4.4 2 92238 2,6 3 MIX-1 10.5 END MIXT Tlus results in mixture i being water at 1.5 density (10019.9 2 and 8016 4.95 2) and mixture 2 is

. highly enriched uraniurr metal, i

EX AMPEES OF INCORRECT USAGE

, (1) READ MIXT MIX-3 1 0.75 MIX-1 2 0.5 MIX.2 1001 6.6 2 8016 3.3 2 END MIXT Ilere the intent is for mixture 2 to be full density water, mixture I to be half density water, and mix-ture 3 to be 3/8 (0.75 x 0.5) density water. Instead, the result for mixture 3 is a void, mixture 1 is half density water, and mixture 2 is full densit," water. This is because the nuclide mixing loop is done first, thus defining rnisture 2. The mixture mixing loop is done next. Mixture 3 is defined to be mix.

ture I multiplied by 0.75, but since mixture I has not been defined,0.75 of zero is zero. Mixture I is then defined to be mixture 2 rnultiplied by 0.5. If the definition of mixture I preceded the definition of mixture 3, as in (2) under examples of correct usage, it would work correctly.

(2) READ MIXT MIX-1 10016.6-2 8016 3.3 2 MIX-100192235 4.4-2 92238 2.6 3 MIX-2 1001 0.5 END MIXT This results in mixture I being' full density water, mixture 1001 being uranium metal and mixture 2 being hydrogen with a number density of 0.5 because 1001 is the nuclide ID number for hydrogen.

When a mixture number is identical to a nuclide ID and is used in mixing, that number is assumed to be a nuclide ID rather than a mixture number. The intent was for mixture I to be full density water, mixture 1001 to be uranium metal, and mixture 2 to be half density uranium metal.

Fil.5.6 GEOMETRY In general, KENO V geometry descriptions consist of (1) geometry data (Sect. Fil.4.4) defining the geometrical shapes present in the problem, and (2) array data (Sect. Fil.4.5) defining the placement of the units that were defined in the geometry data. The geometry data block is prefaced by READ GEOM and the array data block is prefaced by READ ARRAY.

i

- . - , - . , -__ , m -..,_.m y.._ , . , -, . - . . - _ . -. _-_,-,.,.m,-.. . . _ , . . . , _ , , . ~ , . , _ _ , - ...-._ -,..-

l'l1.5.7 When a three dimensional geometrical configuration is described as KENO Y geometry data, it may be neteuary to describe portions of the configuration individually. These individual partial descriptions of the configuration are called units. KENO V Feometry modeling is subject to the following re.itrictions:

(1) I ach geometry region in a unit must completely enclose all geometry regions which precede it.

lioundaries of the surfaces of the reFi ons may be shared or tanfent, but they must not intersect.

(2) All geometrical surfaces must be describable as spheres, hemispheres, cyhnders, hemicylinders, cubes or cuboids.

(3) When one or more units are utilized to demibe un array, each unit used in the array must have a cube or cuboid as its outer region W

(4) When sescral units are utilired to describe an array, the adjacent f aces of units in contact with each other must be the same stic and shape.

(5) As many holes as will snugly fit without intersecting can be placed in a reFi on. lloles cannot intersect each other or any of the regions within the unit they are placed in. Iloles are described in more detail in Sect. 111.5.6.1.

(6) Cornplicated systems may require rnultiple arrays to describe the system. Arrays may be placed in units. These units may be used to create other arrays or may be placed in other units by using holes. Multiple arrays are described in more detailin Sect Fil.5.6.2.

'The geometry package allows any epplicable shape to be enclosed by any other applicable shape, subject only to the complete enciosure restrictmn. The implication of this type of description is that the entire volume between two sequential geometrical surfaces ccntains only one mixtur; unless holes are prescut. Therefore, the entire volume within the surface, defined by the first geometry card ir, a unit, contains the mixture that is specified on that card. The volume between the surfaces, defined by two ,

consecut ve geometry cards, contains the mitture that is specified on the second card. A void is speci- _

fied by a mixture ID of zero. If holes are present in the volume between two surfaces, the volume of that region is reduced by the hole volume (s).

If the problem requires several units to describe its geometrical characteristics, each unit that is used in an array must have as its outer surface a rectangular parallelepiped. Thus, it may be necessary to define a void region that is used to achieve the desired spacing. ,,rder to describe the composite over-all geometrical characteristics of the problem, these units may be arranged in a rectangular array by specifying the number of units in the x, y, and z directions. If me e than one unit is involved, data must be entered to define the number assiF ned to the array and the placement of the individual units in the array. The array number, the number of units in the x, y, and z directions, and the placement data are called array data (Sect. Fil.4.5).

Surrounding regions of any shape may be placed around an array and may consist of any number of regions in any order, subject to the complete enclosure restriction. All of the surrounding regions must be described about a point of origin; consequently, the location of this origin is defined by the ARRAY PLACEMENT description. The surrounding regions are then described relative to this origin.

In addition to array prob! cms, the geometry package allows single unit problems (i.e., problems that do not contain array data). The last geometrical region in a single unit problem need not be a cube or cuboid. lloundary conditions can be apphed to a single unit problem only if the outer region is a ree-tangular parallelepiped. Matris informatwn can be calculated only if the corresponding Feometry

. - - - - - - . . _ . ~ - . - - , - - - - - - - - - - . - . - - - . - - . -

Fl1.5.0 description is utilized in the problem. For example, matrix by hole number requires the utilization $f holes, matrix by array position requires an array, etc.

To create a Feometry mock up from a physical configuration, the user should exercise a degree of ingenuity and keep in mind the restrictions mentioned earlier. It is important to realire there may be several ways of correctly describing the same physical configuration. Careful analysis of the system can pay off in terms of a simpler mock up and shorter computer running tirne. A mock up with fewer geometry regions may run faster than the same mock up with extraneous regions. The number of units or bos types used can affect the running time, because a transformation of coordinates must be made every time a history moves from one unit into another. Thus, if the sire of a unit is small, relative to the mean free path, a larger percentare of time is spent processing the transformation of coordinatcs.

CORE or ARRM: The geometry word CORE was used in KENO IV and earlier versions of KENO Y to create a rectangular parallelepiped that snugly fit the exterior of the array. The purpose of this region was to define the location of the array relative to the geometry regions external to the CORE.

KENO IV and early versions of KENO V allowed only one array in a problem.

I KENO V.a allows rnultiple arrays within a problem, so the geometry word CORE is used to specify the array number of the array, in addition to encasing it in a snug fitting rectangular parallelepiped.

The data that must be entered are the geometry word (CORE), the array number, the bias ID, and the

x. y, and r coordinates of the rnost negative point in the array. The geometry word ARRAY was added to allow specifing the array number and encasing the specified array in a snug fitting rectangular paral-Iclepiped without having to specify the bia; ID. The data that must be entered are the geometry word (ARRAY), the array number, and the x, y, and z coordinates of the most negative point in the array.

The cuthors feel that the Feometry word ARR AY is more descriptive of the function performed, but the geometry word CORE has been retained to allow executing problems that were run on earlier ver-sions of KENO V. '

REFLECTOR or REPLICATE: The geometry word REFLECTOR was used in KENO IV to generate cuboidal regions external to the array. If a snug fitting rectangular parallelepiped (CORE) was not entered in the problem, it was Fenerated by the code. KENO V retained the geometry word REFLEC.

TOR but with a different function it does not generate a snug fitting rectangular parallelepiped (CORE) for an array, and it is not limited to generating cuboidal regions, instead, it generates regions having the shape of the geometry region preceding the REFLECTOR description. The geometry word REPLICATE is used in KENO V.a as a synonym for REFLECTOR. The data is identical for both geometry words and their function is identical. Ilecause these geometry words produce regions having ,

the shape of the previous regions, REPLICATE may be considered to be more representative of the

. actual situation.

Geometry dimensions: The geometry dimensions utilized in KENO have traditionally required an entry for each required dimension. For example, a 20:20x2.5-cm rectangular parallelepiped would have been described as: CUBOID 1 1 10.0 10.0 10.0 -10.0 1.25 1.25. By using the P option (see Table

. Fil.4.2), the same rectangular parallelepiped could be described as: CUBOID 1 1 4P10.0 2Pl.25.

The P option simply adds the dimension following the P, the number of times stated before the P and reverses the sign every other time. 6P8.0 is equivalent to 8.08.08.08.08.0-8.0.

a Geometry Comments: A comment can be entered for each unit in_ the geometry region data. Similarly, a comment can be entered for each array in the array defm' ition data. A comment can be entered using the keyword COM . This is followed by a comment whose maxmum length is 132 characters. The comment must be preceded by and be terminated by a delimiter character, which is the first non blank

character encountered after the COM . One comment is allowed for each unit in the geometry region data, if multiple comments are entered for a unit, the last one is used. The comrnent can be entered J

anywhere after the UNIT NUMBER DESCRIPTION where a keyword is expected (Sect.- Fil.4.4).

See the following example.

I Fi 1.5.9 RE4D GEUAf UNIT l COAL

• SPHERICAL AIETAL UNIT

• SPilERE I I 3.0 CUBE O 12P3.0 UNIT 2 C1'LINDLR I 1 $.0 2P5.0 CURE O 12PS.0 Coal =/Cl'L1NDRICAL AtETAL UNIT /

UNIT 3 HEAllSrilE+ X 11 $.0 COAL.*llEAtlSPHERICAL AIETAL UNIT

• CUBEOI2P3.0 UNIT 4 COAf 'ARRAl' OF SPHERICAL UNITS' ARRA l' I 3*0.0 UNIT $

COAL ~'ARRAl' 0F C)'LINDRICAL UNITS

• ARRA)* 2 3*0.0 UNIT 6 COAf.'ARRAl'0F HEAllSPHERICAL UNITS' ARRA)* 3 3*0.0 END GE0Al One comment is allowed for each array in the ARRAY DEFINITION DATA. The rules governing these comments are the same as those listed above. liowever, the comment for an array must precede the UNIT ORIENTATION DESCRIPTION. It can precede the array number (Sect. Fil.4.5).

Examples of correct array comments are given below.

READ ARRA }'

COAL *ARRA OFSPHERICAL AtETAL UNITS' ARA-1 NUX-2 NU)' 2 NUZ-2 TILL T1 END FILL AR4=2 COAf 'ARRA)'Of C)'LINDRICAL hfETAL UNITS' NUX-2 NU)'-2 NUZ.2 TILL T2 END TILL ARA =3 hUXm2 NUl*=2 NUZ-2 COAL 'ARRAl'0F HEhllSPHERICAL AIETAL UNITS' flLL F3 END TILL ARA =4 Cohl~'COAfPOSITE ARRA 0F ARRAl'S. Z=1 IS SPHERES, Z=2 IS C)'LINDERS, Z.3 IS HEhtl SPHERES' NUX-1 NU)*.I NUZ-3 FILL 4 5 6 END flLL Somest the basics of KENO V geometry are illustrated in the following examples: >

EXAMPLE 1. Assume a stack of six cylindrical disks, each $ cm in radius and 2 cm thick. The bottom disk is composed of material I, and the next disk is composed of material 2.'etc., alternately throughout the stack. A square plate of material 3,20 cm on a side ar ! 5 cm thick, is centered on top of the stack. This configuration is shown in Fig. Fil.5.1.

Fl 1.$.10 m m.,.... e

[ i.

~

,/

x

,/

l

,,l

'-_ p'

/m _A ,

( ,f A ./}

/

-g

.'x , /  ;, x. y 7

' ],

[x ) 'y

[M qu  ;

cmu Fig. Fil.$.l. Stack of disks with a square cap This problem can be described as a single unit problem, by describing the cylindrical portion first, in this instance, the origin has been chosen at the center bottom of the bottom dSk. The bottom disk is' defined by the first cylinder description; the next disk is denned by the difference between the first and secorid cylinder descriptions. That is, since they both have a radius of 5.0 and a z length of 0.0, the first cylinder containing material i exists from z-0.0 to z-2.0 and the second cylinder, containing material 2, exists from z-2.0 to z-4.0. When all the disks have been described, a void cuboid having the same x and y dimensions as the square plate and the same z dimensions as the stack of disks is defined. The square plate of material 3 is then defined on top of the stack. Omission of the Grst cuboid description would result in the stack of disks being encased in a solid cuboid of material 3, instead of having a Dal plate on top of the stack. The geometry input is shown below.

Data description 1. Example 1.

READ GEOM C)*LINDER I i 5.02.0 0.0 C)'LINDER 2 1 3.04.0 0.0 Cl'LINDER I I $.0 6.0 0.0 Cl'LINDER 2 i S.O 8.0 0.0 Cl'LINDER I 1 $.010.0 0.0 C1'LINDER 2 1  :.0 12.0 0.0 CUBotD 0110.0 10.010.0 10.012.00.0 CUBolD 3110.0 10.010.0 10.014.50.0 An alternate description of the same example is given below. The origin has been chosen at the cen-ter of the disk of material 1, nearest the center of the stack. This disk of material I is defined by the first cylinder description, and the disks of material 2 on either side of it are defined by the second cylin-der description. The top and bottom disks of material I are defined by the third cylinder, and the top disk of material 2 is defined by the last cylinder. The square plate is defined by the two cuboids.

Data description 2, Example 1.

I l

q 1

, . - . , . . . . , , , , . . . _ . _ ~ ~ , , , ._ . . - -. . , . , . ,.

i 11.5.1 i REiD GLOAl C1'LINDER I I 5.0 1.01.0 C)*LINDER 21 $.0 3.0 3.0 C)*LINDER 1 I 5.0 5.0 .$.0 C1'LINDER 21 3.0 7.0.$,0 CullulD 01 10.0 10.010.0 10.0 7.0 .$.0 CUBOID 31 10.0 10.010.0 -10.0 9.5 .$.0 1;xample i can also be described as a bare array. Define three different unit types. Unit I will define a dak of material 1. Unit 2 will define a disk of material 2. and Unit 3 will define the square plate of material 3. The origin of each unit is defined at the center bottom of the disk or plate being described The geometry input for this arranfernent is shown below.

Data description 3, Examr'e 1.

READ GLOAl UNITI Cl'LINDER I i 3.0 2.0 0.0 CUBOID 0110.0 10.010.0 10.02.00.0 UNIT 2 C)'LINDER 21 3.0 2.0 0.0 CUB 0!D 0110.0 10.010.0 10.02.00.0 UNIT 3 CUBUID 3110.0-10.010.0 10.02.50.0 END GE0Al RE4D ARRA)* NUX-I NU)'-I NUZ-7 FILL I 21212 3 END ARRAl' If the user wishes the origin of each unit to be at its center, the geometry region data can be input as shown below. The array data would be identical to that of data description 3, Example 1.

~

Data description 4, Example 1.

READ GE0h!

UNIT 1 C)'LINDER I 1 3.0 1.01.0 CUBOID 0110.0 10.010.0 10.01.0.l.0 UNIT 2 C)'LINDER 21 $.0 1.01.0 CUBolD 0110.0-10.010.0 10.01.0.l.0 UNIT 3 CUBotD 3 1 10.0 -10.0 10.0 -10.0 1.25 1.25 END GEOAl Be aware that each unit in a geometry description can have its origin defined independent of the other units. It would be correct to use Units I and 3 from data descriptions 3, and Unit 2 from data description 4. The array data would remain the same as data description 3, Example 1. The user should define the origin of each unit to be as convenient as possible for the chosen description.

1:11.5.12 Another method of describing Example I a. a bare array is to define Unit i to be a disk of material 1, topped by a ditk of rnaterial 2. The origin has been chosen at the center bottom of the disk of mate.

rial 1. Unit 2 is the square plate of material 3 with the origin at the center of the unit. The array con-sists of three Unit l*s, topped by a Unit 2 as shown below.

Data descriptien 5. Example 1.

RL4D GEDAf UNil I C1'LINDER I I S.O 2.0 0.0 C)'LINDER 21 3.0 4.0 R0 CUBolU U l 10.0 10.0 IVO 10.0 4.0 0.0 UNIT 2 CUBolD 3110.0 10.010.0 10.01.25 1.25 END GEUAI RL4D ARRA)' NUX-I NU)*-1 NUZ-4 TILL 3RI 2 END ARR41' Example I can be described as a reflected array by treating the square plate as a reflector in the positive z direction. One means of describing this situation is to define Units 1 and 2 as in data description 3, fixample 1. The origin of the core boundary is defined to be at the center of the array.

The correr.ponding input geometry is shown below.

Data description 6, Example 1.

READ GEDAf UNITI C)'LINDER I I 3.0 2.0 0.0 CUBolD O I 1R0 IRO 10.0 -10.0 2.0 0.0 UNIT 2 C)'LINDER 21 5.0 2.00.0 CUBulD 01 10.0-10.010.0 l&O2.0 0.0 CORE O I 10.0 -10.0 -6.0 CUB 0!D 31 10.0-10.010.0-10.08.5 6.0 END GEDAf READ ARRAl' NUX.I NU)' I NUZ.6 FILL i 2 I 212 END ARRAl' The user could have chosen the origin of the core boundary to be at the center bottom of the array.

The last two cards would then be:

CORE O I I V 0 10.0 0.0 CUBulD 3110.0 10.010.0 10.014.50.0 A simpler method of describing Example I as a reflected array is to define only one unit as in data description 5, Example 1. Tbc square plate is treated as a reflector as in data description 6, Example 1.

The input for this arrangement is given below.

1:11.5.13 4

Data description 7. Example 1.

READ GE0Af C)'LINDER I I 5.0 2.0 0.0 Cl'LINDER 21 3.0 4.0 0.0 CUBOID 01 10.0 10.010.0 10.04.00.0 CORE OI10.010.00.0 CUBulu 31 10.0 10.010.0 -10.014.$ 0.0 END GLOSI RL4D ARRAl' NUX I NUl'-I NUZ-3 END ARRAl' Note that the unit onentation data need not be entered in the array data if only one unit is defined in the Feometry region data. Similarly, a umt or bot. type definition need not be entered when only one unit is defined EXAMPLE 2. Assume the stack of six disks in Example 1 is placed at the center bottom of a cyhndrical container composed of material 6 whuse inside diameter is 16.0 cm. The bottom and sides of the container are 0.25 cm thick, the top is open and the total height of the container is 18.25 cm.

Assume the square plate of Example I is centered on top of the container.

The geometry input can be described utilizing most of the data description methods associated with inample 1. One method of describing Example 2 as a single unit is 1.iven below.

Data description I, Exampic 2.

RL4D GEOAf C)*LINDER I 1 3.0 1.0 -l.0 C)'LINDER 21 3.0 3.0 3.0 C)'LINDER I 1 $.0 5.0 -$.0 C)*LINDER 21 $.0 7.0 $.0 C)'LINDER 01 8.0 13.0 $.0 C)'LINDER 6 I 8.25 13.0 $.23 CUB 0lD 0110.0 10.0 10.0 -10.013.0 $.23 CUBO!D 3110.0 -10.0 10.0 10.015.5 $.25 END GEOSI in the above description, the origin is defined to be at the center of the disk of material I nearest the center of the stack. This disk is defined by the first cylinder description. The disks of material 2 above and below it are defined by the second cylinder description. The disks of material 1 above and below them are defined by the third cylinder description. The top disk of material 2 is defined by the fourth cylinder description. The void interior of the container is defined by the fifth cylinder descrip-tion. The container is defined by the last cylinder descrip; ion. The first cuboid card is used to define a void whose x and y dimensions are the same as the square plate, and whose z dimensions are the same as the container. The last cuboid card defines the square plate. Omission of the first cuboid card would result in the container being encased in a solid cuboid of material 3. Thus, both cuboids are nec-essary to properly define the square plate.

I

s Fil.5.14 Esampic 2 can be described as a reflected array. One of the descriptions uses only one unit and is similar to data description 7, example 1. This is shown below. Note that the use of only one unit type allows omission of the Unit type definition and the unit orientation data.

Data description 2, Example 2.

READ GE0Af C)'LINDER I I 3.0 2.0 0.0 CYLINDER 2 I $.0 4.0 0.0 CUBulD 0 I $.0 -$.0 $.0 .$.0 4.0 0.0 CORE O 1 $.0 .$.0 0.0 C)*LINDER 01 8.0 18.0 0.0 C)'LINDER 61 8.25 18.0 0.25 CUButD 0110.0 10.0 10.0 10.018.0-0.23 CUBOIU 3110.0 10.0 10.0 -10.020.5 0.25 '

END GEUAf READ ARRAl' NUX=1 NUl'= I NUZ-3 END ARRAl' In this data description, the first two cylinder descriptions define a disk of material I with a disk of material 2 directly on top of it. A tight fitting void cuboid is placed around them rio they can be stacked three high to achieve the stack of disks shown in Example 1 Fig. Fil.5.1. This array comprises the core or array portion of the geometry region description. The origin of the core bound-ary, a tight fitting cube or cuboid that encompasses the core, is defined by the CORE description.

Everything after the CORE desenption is considered part of the reflector. The first cylinder after the CORE defines the void interior of the cylindrical container. The next cylinder defines the walls of the container. The next to last cuboid defines a void volume outside the container from its bottom to its top and having the same x and y dimensions as the square plate. The last cuboid defines the square plate of material 3 that is sitting on top of the container.

Example 2 cannot be described as a reflected array if the inner radius of the container is smaller than 7.071 cm (V22$.02 ). This is the radius at which the inner boundary of the container is tangent to the cuboid around the disks. If the inner radius is smaller than 7.071 cm, the data must be described as a single unit; or alternatively, the container must be included within the units. Anume the container of Example 2 has an inner radius of 6.0 cm with all other data remaining the same. An example of the rcometry data describing this configuration is given below in data description 3, Example 2.

Data description 3, Example 2.

READ GEOh!

UNIT l CYLINDER 616.25 0.25 0.0 CUBotD 0110.0 -10.0 10.0 10.00.25 0.0 UNIT 2 C)'LINDER I I $.0 2.0 ' O.0 C)'LINDER 21 5.0 4.0 0.0 C)'LINDER 01 6.0 4.0 0.0 C1'LINDER 61 6.25 4.0 0.0 CUBotD 0110.0 -10.0 10.0 -10.0 4.0 0.0 UNIT 3 Cl'LINDER 01 6.0 3.0 -3.0 Cl'L1NDER 61 6.25 3.0 3.0 CUBolu 0110.0 40.0 10.0-10.03.0 3.0 CUBotD 3110.0 -10.0 10.0 10.03.5 3.0 END GE0Af READ ARRAl' NUX-I NUl' I NUZ-$ TILL i 3R2 3 END ARRAl'

___ _ m_ _ _ ._ _ . _ _ _ _ _ . . _ _ _ , . . - _ . . - _ _ _ _ _ _ . . - _ . . _ . - _ . _ _ _ _

Fi l.5.15 in the above description, Unit I is the bottom of the cylindrical container. The void cuboid is only as tall as the bottom of the container, and its x and y dimensions are the same as the square ;> late on top of the container. If all the units in the array utilire these same dimensions in the x and y direc.

tions, the restriction that adjacent faces of units in contact with each other be the same site and shape is satisfied. This array is stacked in the z direction, so all units must have the same metall dimensions in the x direction and in the y direction. Unit 2 will be used in the array three times to create the stack of disks. It contains a disk of material 1, topped by a disk of material 2. 'the portion of the container that contains the disks and the cuboid that defines the outer boundaries of the unit are included in Unit

2. Unit 3 describes the empty top portion of the container and the square plate on top of it. The r dimensions of Unit 3 were determined by subtracting three times the total t dimension of Unit 2 from the inside heiF ht of the container [18.0 - (3 4.0) - 6.0}. This can also be determined from the over.

all height of the container by subtracting off the bottom thickness of the container and three times the height of Urut 2 (18 25 0.25 . (3x4.0) - 6,0J. The origm of Unit 3 is located at the center of this distance. If the ori Fin were chosen at the bottom of that height,it would be described as:

UNIT 3 Cl'L1NDER 01 6.0 6.0 0.0 C)'LINDER 61 6.25 6.00.0 CUButD 01 IILO 10.010.0 10.0 6.0 0.0 CUBUID 3110.0 -10.010.0 10.08.250.0 liX AMpLli 3. Refer to lixample I, Fig. Fil.5.1, and imagine a hole 1.5 cm in diameter is drilled along the centerline of the stack through the disks and the square plate. This climinates the possibility of describing the system as a single unit. This is because the hole in the center of the alternating materials of the stack cannot be described in a manner that allows each successive geometry region to encompass the regions interior to it. Therefore, it must be described as an array. The square plate on the top of the disks is defined as a unit in the array. In the geometry description given below, the j- square plate is defined in Unit 3.

Data description I, Iixample 3.

READ GE0h!

UNITI

C1'LINDER 01 0.75 2.0 0.0 C)'LINDER I I 5.0 2.0 0.0 l CUBOID 0110.0 -10.010.0 10.02.00.0 t

UNIT 2 l C1'LINDER 01 0,75 2.0 0.0 C)'LINDER 21 5,0 ' 2.0 0.0 CUBolu 0110.0 10.010.0 10,02.00.0 UNIT 3 Cl'LINDER 01 0,73 2.5 0.0 CUBotD 3110.0 -10.010.0-10.02.50.0 END GEOh!

READ ARRA)' NUX~l NU)*=1 NUZ-7 FILL I 2 202 3 END TILL END ARRA)' .

In data description 1, Example 3 above, Unit I describes a disk of material I with a hole through its centerline. The first cy!inder defines the hole, the second defines the rest of the disk, and the cuboid defines the site of the unit to be consistent with the square plate so they can be stacked together in the

) array. Unit 2 describes a disk of material 2 in similar fashion. Unit 3 describes the square plate of l material 3 with a hole through its center. The cylinder defines the hole and the cuboid defines the l

l

_ . _ _ ___m . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . . _ _ _ _ _ _ . _ _ . . _ _ . _ . . _ _

i Fi l.5.16 square plate. These three units are stacked in the z direction to achieve the composite system. This is represented by FILL 1 2 2Q2 3. The 2Q2 repeats the two entries preceding the 2Q2, two times.

Alternatively, thir can be achieved by entering FILL 1 2 1 2 1 2 3 END FILL. The same array can also be achieved using ihe LOOP option. An example of the data for this option is:

LOOP 1 6RI 152 2 6R1 2 6 2 3 6R1 7 7 I END LOOP. Unit 1 is placed at the x-1, y-1 and z-1,3,5 positions of the array by entering 16R1 1 5 2. Unit ' is e positioned at the x-l, y- 1 and z-2,4.6 positions in the array by entering 2 6R1 2 6 2. Unit 3 is placed at the x-1, y 1, z-7 position of the array by entering 3 6R17 71. See Sect. Fil.4.5 for additionalinformation regarding array specifications. Table Fil.4.2 lists other available input options.

EX AMPLE 4. Assume two larFe cylinders, 2.5 cm in radius and 5 cm long, are connected by a smaller cylinder,0.5 cm in radius and 10 cm long, as shown ir Fig. Fil.$.2. All of the cylinders are composed of material 1. Ily starting the Feometry description in the small cylinder, this system can be described as a single unit.

e .-3.: .. or

,' ^- l~ h- --._%.

.= ,I 'w -

r_ . - _ .

( )

x ,) - L)

.- N :! .-

)

Fig. Fil.5.2. Two large cy"iders joined axially by a small cylinder t

Data description 1, Example 4.  !

READ GEOh!

C)'LINDER I I 0.5 3.0 .$.0 Cl'LINDER 012.$ 5.0 .$.0 C1'LINDER I I 2.510.0 10.0 END GE0ht '

The origin is at the center of the small cylinder which is described by the first cylinder card. The second cylinder card defines a void cylinder surrounding the small cylinder, its radius is the same as the large cylinders, and its height coincides with that of the small cylinder. The last cylinder card defines the large cylinders on either end of the small cylinder.

EXAMPLE 5. Assume two large cylinders with a center-to-center spacing of 15 cm, each having a radius of 2.5 cm and length of 5 cm, are connected radially by a small cylinder having a radius of 1.5 cm, as shown in Fig. Fil.5.3.

i Fi 1.5.17 .

m. a s e . ....

f [M s.

,%y

)

p 7--

, .- -...-- - - - - - _ ~ .

-- 4 i

,O k , I e ,, , s N. _ %s Fig. Fil.5.3. Two lay .mders radially connected by a small cylindes This system cannot be rigorously described in KENO V geometry because the'iritersection of the cyhnders cannot be described. Ilowever, it can be approximated two ways, as shown in Fig. Fil.5A.

The top approximation is described in data description 1, example 5. The bottom approximation is described in data description 2, example 5, and data description 3, example 5. These may be poor approximations for criticality safety calculations.

ORNL- DWG 83-43259 TOP VIEW FRONT VIEW END VIEW 4

?

%,l

- w

! l I 4 l q, _g ,- ..- ._

g-y j l' p . .m .

Fig. Fil.5A. KENO V approximations of cylindricalintersections Data description 1. Example 5.

READ GE0ht UNIT 1

l. Cl'LINDER I I 2.52.3 2.5

CUBE O12.5 2.5 l UNIT 2 l XC)*LINDER 1 1 1.5 $.0 $.0

. CUBOID 015.0 $.0 2.3 -2.5 2.5 -2.5 l END GE0h!

READ ARRAl' NUX-3 NU)'=1 NUZ-1 FILL 121 END ARRA)'

i l

(-

l

-wy .- e , , , . , ,_,_.--.--,.w-- -- -, ,w --r-w , w ,, . .- -

Fl 1.5.18 Unit I defines a large cylinder, and Unit 2 describes the small cylinder. In both units the origin is at the center of the cylinder.

Data description 2. Example 5.

RC4D GE0AIETRl' UNIT l C1'LINDER I I 2.31.00.0 CUB 010 014P2.51.0 0.0 UNIT 2 ZHEAllCh'CL X 112.5 2Pl.3 CHORD 2.0 CUBUID 0120 3P 2.$ 2Pl.3 UNIT 3 ZilEhflC1'L+ X 112.5 2Pl.3 CHORD 2.0 CUBOID 012.3 2.0 2P2.5 2Pl.$

UNIT 4 XC1'LINDER I i 1.3 2PS.$

CUBolD 0102PS.$ 2P2.5 2PLS UNIT $

CUBotD 012PS.O 2P2.3 LO 0.0 UNIT 6 A RRA l' 1 3

• 0.0 UNIT 7 ARRAl' 2 3*0.0 END GEOSIETRl' RE4D ARRAl' ARA =1 NUX=3 NU)'=1 NUZ=1 FILL 1 $ 1 END FILL ARA = 2 NUX=3 NU)'=1 NUZ-1 FILL 2 4 3 END FILL ARA =3 NUX=1 NU)'=1 NUZ=3 TILL 6 7 6 END FILL END ARRAl' This geometry description uses arrays oi arrays (see Section Fil.5.6.3) to describe the bottom approxi-mation of Fig. Fil.5.4. Unit I defines a large cylinder 2.5 cm in radius and 1.0 cm tall inside a close fitting cuboid. This is used in both large cylinders as the portion of the large cylinder that exists both above and below the region where the small cylinder joins it. Unit 5 is the spacing between the tops of the two large cylinders and the spacing between the bottoms of the two large cylinders. Array 1 thus defines the bottom of the system: two short cylinders (Unit l's) separated by 10 cm (Unit 5 is the sepa-ration). Unit 6 contains array 1.

Unit 2 is the left 'hemicylinder' that adjoins the horizontal cylinder, and Unit 3 is the right 'heini-cylinder

• that adjoins the horizontal cylinder. Unit 4 defines the horizontal cylinder. Array 2 contains Units 2,4, and 3, left to right. This defines the central portion of the system where the horizontal cylin-der adjoins the two 'hemicylinders.' Thesc *hemicylinders" are larger than half cylinders. Unit 7 con-tains array 2.

The entire system is achieved by stacking a Unit 6 above and below the Unit 7 as defined in array 3, the global array.

Data description 3, Example 5.

Fi l.5.19 RE4D GE0AfETRl' UNITI C1'LINDER I 12.$ !.0 0.0 UNIT 2 C1'LINDER 1 1 2.$ 1.0 0.0 CUBolD O I 17.$ 2.$ 2P2.$ 1.0 0.0 HOLE I I3.0 0.0 0.0 UNIT 3 Zill'AllC)'L X 112.$ 2Pl.$ Cil0RD 2.0 UNIT 4 Z.lEAllC)'L +X 112.$ 2Pl.$ CHORD 2.0 UNIT $

XC)'LINDER 1 I l.$ 2P3.5 CUBolu 01 2Plu.0 2P2.$ 2Pl.3 il0LE 3 7.$ 2*0,0 HULE 4 7.3 2*0.0 END GEUAlETRl' READ ARR4l' ARA-1 NUX-1 NU)'-l NUZ-3 Til.L 2 3 2 END TILL END ARRA)*

This geometry description uses holes (see Sect. Fil.5.6.1) to describe the bottom approximation of l ig. Fi l.4. Unit I defines a large cylinder 2.5 cm in radius and 1.0 cm tall. Unit 2 defines the same cylinder within a cuboid that extends from x- 2.5 to x-17.5, fromy- 2.5 to y-2.5, and z-0.0 to z - 1.0. The origin of the cylinder is at (0.0,0.0.0.0). Thus Unit 2 describes the top and bottom of the cylinder on the left. Unit 1 is positioned within this cuboid as a hole with its origin at (15.0.0.0,0.0) to describe the top and bottom of the cylinder on the right. Unit 3 is the left "hemicylinder' that adjoins the horizontal cylinder, and Unit 4 is the right "hemieylinder* that adjoins the horizontal cylinder. Unit 5 defines the horizontal cylinder with its origin at the center within a cuboid that extends from x 10.0 to x- + 10.0, y- 2.5 to y-2.5, and z- l.5 to z- 1.5. Unit 3 is positioned to the left of the horizontal cyl-inder, and Unit 4 is positioned to the right of the horizontal cylinder by using holes.

The entire system is achieved by stacking a Unit 2 above and below Unit 5 as shown in the array data.

This same geometry description can be used with Unit 2 redefined to have its origin defined so the unit extends from x- 10 to x-10, y- 2.5 to y=2.5, and z-0.0 to z-1. In this instance, the geometry data would be identical except for Unit 2. This alternate description of Unit 2 is:

UNIT 2 C)'LINDER I 1 2.5 1.0 0.0 ORIGIN 7.3 0.0 CUBOID 012Plo.O 2P2.51.0 0.0 HOLE 17.$ 0.0 0.0 EX AMPLE 6. Assume 2 small cylinders 1.0 cm in radius and 10 cm long are connected by a large cylinder 2.5 cm in radius and 5 cm long as shown in Fig. Fil.5.5.

Fi l.5.20 O ow . o* c, w 4 88 2 yJ

/ j b Os ,)

t,'hw4'[

! i!

ll i

}

\; . ./

Ml O

l'ig. Fil.5.5. Two small cylinders joined axially by a large cylinder This problem is very similar to exampic 4, but it cannot be described as a single unit, it must be described as an array. Unit i defines the large cylinder, and Unit 2 defines the small cylinder. The origin of each unit is at its center. The composite system censists of two Unit 2's and one Unit I as shown below.

Data description 1 Example 6.

RC4D Gl;Oh!

UNITI C1'LINDER I I 2.$ 2.3 2.3 CUBE O I 2.3 2.5 UNIT 2 C)*LINDER I i 1.0 5.0.$.0 CUB 0lD 0 1 2.5 2.$ 2.5 2.$ 5.0 .$.0 END GE0h!

READ ARRA1' NUX=1 NU1*.I NUZ-3 TILL 212 END ARRA1' EXAMPLE 7. Assume an lix5x3 array of spheres of material 1, radius 3.75 cm, with a center to-center spacing of 10 cm in the x, y, and z directions. The data for this system are given below.

Data description I, Example 7.

READ GE0h!

SPilERE i 13.75 CUBE OI5.0.$.0 END GE0h!

READ ARRA1'NUX 1I NU1'-3 NUZ-3 END ARRA1'

F i l .5.21 EX AMPLE 8. Assume an lix50 array of spheres of material I whose radius is 3.75 cm, and whme center to-center spacing is 10 cm in the x direction,15 cm in the y direction, and 20 cm in the i direction. T he input for this geometry is given below.

Data description I. Example 8.

RL4D GEUAl SI'llERE I I 3.75 .

CUBOID 0 I $.0 -$.0 7.3 7.510.0 10.0 END GLOAl RL40 ARR41' NUX Il NUY-$ NUZ-3 END ARR41' EX AMPLE 9. Av.ume an lix50 array of spheres of material I whose radius is 3.75 cm, and whose center to-center spacing is 10 cm in the x, y. and r directions. This array is renected by 30 cm of material 2 (water) on all f aces. The array spacing defines the perpendicular distance from the outer layer of spheres to the reflector to be 5 crn in the x, y, and 7 directions. The geometry input for this system is given below.

Data description 1, Exarnple 9 RL4D GEUAl SI'HERE II 3.75 CUBE O1 3.0 $.0 CORE O I $$.0 23.0 l$.0 REFl.ECTOR 226*3.0 10 END ARRAl' READ ARRAl' NUX-1I NU)'-$ NUZ= 3 END ARIUl' READ B!AS ID-500 2 !! END DIAS The core boundary defines the origin of the reDector to be at the center of the array. The 6*3.0 on the reDector card repeats the 3.0 six times. The reDector card is used to Benerate ten reflector regions, each 3.0 cm thick, on all six faces of the array. The first bias ID is 2. so the last bias ID will be 11 if 10 regions are created. The biasing data bkek is necessary to apply the desired weighting or biasing function to the reflector. The biasing material ID is obtained from Table Fil.4.5. If the biasing data block is omitted from the problem description, the 10 renector regions will not have a biasing function applied to them, and the default value of the average weight will be used. This may cause the problem to execute more slowly, and therefore require the use of more computer time.

EXAMPLE 10. Assume the reflector in Example 9 is present only on both x faces, both y faces, and the negative r face. The renector is only 15.24 cm thick on these faces. The top of the array (pos-itive z face)is unreDected.

Data description 1, Example 10.

READ GE0Al SI'llERE II 3.75 CUBE OI $.0 -$.0 CORE O I $$.0 -25.0 l$.0 REFLECTOR 2 2 4*3.0 00 3.0 $

RETLECTOR 274*0.24 0.0 0.24 i RE4D ARRA)'NUX 1I NUV-$ NUZ 3 END ARRAY READ BIAS ID=$00 2 7 END BIAS

Fi 1.5.22 The first renector card generates five regions around the array, each region being 3.0 cm thick in  :

the + x, .x, + y, y. and r directions, and of reto thickness in the + r direction. This defines a total thickness of 15 cm of renector material on the appropriate faces. The second reflector card generates .

the last 0.24 cm of material 2 on those faces. Thus, the total renector thickness is 15.24 cm on each face of the array, except the top which has no renector. Five reflector regions were generated by the first renector card, and one was generated by the second reflector card; so, six biasing regions must be defined in the biasing data _ Thus, the beginning bias ID is 2, and the ending bias ID is 7. The biasing material ID and thickness per region are obtained from Table Fil.4.5. The thickness per region should be scry nearly the thickness per region from the table to avoid overbiasing in the tenector. Partial increments at the outer region of a reflector are exernpt from this recommendation. If a biasing func-tion is not to he applied to a region generated by the reflector card, the thickness per region can be any desired thickness. In this instance, a biasing data block is not entered.

EXAMPLL 11. Assume the array of example 7 has the central unit of the array replaced by a cyl-inder of material 4,5 cm in radius and 10 cm tall. Assume a 20-cm thick spherical reflector of mate-rial 3 (concrete) is positioned so its inner radius is 65 cm frc.m the center of the array. The minimum inner radius of a spherical renector for this array is 62.25 cm (J55 +252 +152). If the inner radius is smaller than this. the problem cannot be described using KENO V geometry.

Data description 1, Example 11.

READ GE0h!

UNITI SI'HERE I I L75 CUBE O 13.0 -$.0 UNIT 2 Cl*l.INDER 4130 $.0 LO CUBEOi50 5.0 CORE O 1 5LO 250 130 SI'llERE O 165.0 REl'LICATE 3 2 30 4 END GE0ht READ ARRA)* NUX-il NU)' $ NUZ-3 LOOL' I i il I i $ ! ! 31 266133122 i END ARRA)'

READ BIAS ID=3012 $ END BIAS Unit I describes the sphere and spacing utilized in the array. Unit 2 defines the cylinder that is located at the center of the array. The CORE defines the origin of the reflector to be at the center of the array. The sphere following the core card defines the inner radius of the reflector, The replicate card will generate four spherical regions of material 3, cach 5.0 cm thick. The first 10 entries following i the word LOOP fills the lix5x3 array with Unit 1. The next 10 entries position Unit 2 at the center of-the array (x=6, y-3, and 2-2), replacing the Unit I that had been placed there by the first 10 entries.

The biasing data block is used to apply the biasing function for concrete to the generated reflector regions.

i EXAMPLE 12. Assume a data profile such as fission densities is desired in a cylinder at'l-cm intervals in the radial direction and 1.5-cm intervals axially. The cylinder, composed of material 1, has a radius of 15 cm and a height of 45 cm. The REPLICATE description can be used to generate these regions as shown below. A biasing data block is not entered because default biasing is desired through-out the cylinder.

F11.5.23 Data description I, Example 12.-

Ribill GE0h!

CYl.INI)ER I I 1.01.5 -1.5 REPLICATE I 21.0 2*l.$ 14 ENI) GEUAl Yll.$.6.1 Use oflloles in the Geometry Section Fil.$.6 tells how each KENO Feometry region in a unit must completely enclose all previ-ously described regions in that unit. lloles can be used to circumvent this restriction to sorne degree.

A IlOLE is a means of placing an entire unit within a geometry region. A separate llOLE description is required for every location in a geomet:y region where a unit is to be placeds The information contained in a hole description is: (1) the geometry word, llOLE, (2) the unit nurnber of the unit to be placed, and (3) the x, y, and r coordinates specifying where the origin of the placed unit is to be h>cated. A hole is placed inside the geometry region that precedes it (excluding holer. . . i.e., if a CUllE geometry region is followed by four llOLE descriptions, all four of the llOLES are located within the CUllE.) lloles are subject to the restriction that they_ cannot intersect any other geometry region. lloles can he nested to any depth (see Sect. Fi1.5.6.2). -

Tracking in regions that contain holes is less efficient than tracking in regions that do not contain holes. Therefore holes should be used only when the system cannot be casily described by conventional methods. One example of the use of holes is shown in Fig. Fil.$.6.

The large rods are 1.4 cm in radius and composed of mixture 3. The small rods are 0.6 cm in radius and composed of mixture 1. The inside radius of the annulus is 3.6 cm, and the outside radius is 3.8 cm. The annulus is rnade of mixture 2. The rods and annulus are both 30 cm long. The annulus is centered in a cuboid having an 8-cm square cross section and a length of 32 cm. All nonshaded areas are void. In this mock up, a small rod is defined by Unit I and a large rod is defined by Unit 2. Unit 3 defines the central small rod, the annulus and the cuboid. Units I and 2 are placed within the annu-lus using holes.

i 1

.-v- . , - , = . , . M m. - - . 5---,- ,w - - - , . , ,,,r' . ' . .-.

_ _ . . _ . _ _ _ . _ . ~ . _ _ _ _ . . . . _ . . - . _

i Fil.5.24 OR N L-DWG 83-10284

,s ss s ux s o ..

o s

's s s s s

1 x s

• \

i s . x

[ 4

• i

. j/ ,

.  : ,1/';,1 s

, s .s' .. .  : .:. .. : . .:

s

/ ;J  : '.~. ' . *

,; s

,i j f:'j.j.:

y y- .

. . + ' . . .* :. : .-

)),-

x j  % .

\ .

i ..

1 l y

\ p. x '

d \ i, /),,

e

'N x b- _,, #  !

M-E x Mgxxxxxxxs s '

Fig. Fil.5.6. Close packed rods in an annulus

., . . . . - .. .;-..-._ . = . . ..

Fi 1.5.25 The geometry mock.up can be given by:

READ GEOM UNIT l C)'LINDER 110.6 2Pl3.0 UNIT 2 C)'LINDER 311.4 2Pli.0 UNIT 3 C)*LINDER 110.6 2Pl$.0 C)'LINDER 013.6 2Pl$ 0 '

fl0LE 2 0.0 2.0 0.0 il0LE I 2.0 -2.0 0.0 H0LE 2 2.0 0.0 0.0 Il0LE I 2.0 2.0 0.0 HOLE 2 0.0 2.0 0.0 fl0 Lli ! 2.0 2.0 0.0 IIOLE 2 2.0 0.0 0.0 ll0LE I 2.0 2.0 0.0 C)'LINDER 213.5 2Pl$.0 CUBotD 014P4.0 2Pl6.0 END GEOM READ ARRAl' NUX-1 NUl'.I NUZ-1 FILL F3 END ARRAl' The first ilOLE description is for the bottom large rod. It says to take Unit 2 and place its origin at (c ',2.0.0.0) in Unit 3. The second llOLE description is for the small rod to the right of the large rod just discussed, it places the origin of Unit I at (2.0,-2.0,0.0) in Unit 3. The third '10LE description is for the la;ge rod to the right. It places the origin of Unit 2 at (2.0.0.0,0.0) in Umt 3. This procedure is repeated in a counterclockwise direction until all eight rods have been placed within the region that defines the inner surface of the annulus. The CYLINDER that defines the outer surface of the annulus is described after all the holes for the previous region have been placed. Then the outer cuboid is described.

This example illustrates that a unit that is to be placed using a llOLE description need not have a cube or cuboid as its last region.

An alternate mock up for this problem would be to omit the first region in Unit 3 and put it in as a hole. The hole description for the central rod would be: llOLE I 3*0.0.

The order of the 110LE cards in any given region is not important (they can be interchanged with each other randomly). Ilowever, they must always appear immediately after the region in which they are placed.

An array of the arrangement shown in Fig. Fil.5,6 can be easily described by altering the array description data. For example, a 5x3x2 array of these shapes with a center to-center spacing of 8 cm in x and y and 32 cm in z can be achieved by utilizing the following array data:

READ ARRA)* NUX 5 NU)*-3 NUZ-2 FILL F3 END FILL END ARRAY or READ ARRA)' NUX S NU)' 3 NUZ-2 FILL 30*3 END FILL END ARRA)'

or READ ARRA)' NUX-S NUY-3 NUZ-2 LOOP 315 I i 3 I I 21 END ARRA)*

- - ._ _ .~ _ _ , __. ._ _ . _ _

Fi l.5.26 l

Another example of the use of holes is shown in Fig. Fil.5.7.

I OR NL-DWG 83-10098

// ' '

/ ..

'1I/ e j

/

' /

/ /

l 1

/

/ ' ,'

/ x

/ / _

? / \

/

, / ./'

i

. // s' Z /D  %

/

/

h , 'y/

// /N ' /

>x ,

/ /

Fig. Fil.5.7. Annular rods in triangular pitch lattice Assume that an infinite linear array of annular rods are stacked three high in a triangular pitch.

The array is infinite in the x direction, and the annular rods are stacked three high in the z direction.

The rods are finite in the y direction and stacked only one deep in y. The pitch is di. This array can be created by describing the geometrical arrangement shown in Fig. Fil.5.7 and applying specular or mirror image reflection on both x faces.

The annular rods are all composed of mixture number one, have an inside radius of 1.3 cm, an out-side radius of 1.6 cm, and are 24 cm long. The pitch is di, approximately 3.606 cm. This system can be described in many ways.

This geometry mock up assumes the origin of the basic unit to be on the left face ( x face), halfway up the cuboid. This is defined as Unit 1. Unit 2 is a hemicylindrical annulus which will be placed along the right face (+x face) using holes.

1 Fi 1.5.27 RIMD GEGAl UNITI YllEAllC1'L+h 011.3 2P12.0 l'IlEAllC)'L+X 111.6 2P12.0 CUBOID 012.0 0.0 2PI2.0 2P3.0 HOLE 2 2.0 3.0 0.0 Il 0 L E 2 2.0 3.0 0.0 UNIT 2 l'HEAllC)'L X 011.3 2P12.0 l'HEAllC1'L X i i 1.6 2P12.0 END GEUAl READ ARRAl' NUX-1 NUl' I NUZ-I flLL FI END ARRA}'

RibtD BOUNDS XTC. AllRROR END BOUNDS In the above geometry description, the hernicylindrical annulus on the left ( x face) is described in Unit 1. A hemicyhndrical annulus that is oriented in the opposite direction is described in Unit 2.

The first ilOLE description locates the origin of Unit 2 at (2.0,.3.0,0.0) in Unit 1. This positionr the lower hemicylindrical annulus as shown in Fig. Fil.$.7. The second llOLE description locates the ori-gin of Unit 2 at (2.0,3.0,0.0) in Unit 1. This positions the top hemicylindrical annulus as shown in the figure. The two holes can be interchanged without altering the results. The order in which holes are described is not important.

If Units I and 2 are interchanged, the geometry mock up would .>e as follows: ^

READ GEDAf UNITI l'HEAllCl'L-X 01 1.3 2P12.0 l'HEAllC1'L.X l G 1.6 2Pl2.0 UNIT 2 1'HEAflC1'L+X 01 1.3 2P12.0 l'HEntICl'L+X l i 1.6 2PI2.0 CUBotD 01 2.0 0.0 2P12.0 2P3.0

• HOLE I 2.0 3.0 0.0 HOLE I 2.0 3.0 0.0 END GE0Af READ ARRAl' NUX=1 NU)'=1 NUZ=1 FILL F2 END ARRAl' READ BOUNDS XTC=hilRROR END BOUNDS In the above mock up, Unit 2 describes the hemicylindrical annulus on the left and the cuboid -

exactly as Unit I did in the previous geometry description. Unit I now describes a hemicylindrical annulus that is oriented in the opposite direction (exactly the same as Unit 2 in the previous descrip-tion). The first ilOLE description places the origin of Unit I at (2.0,3.0,0.0) in Unit 2. The second flOLE description places the origin of Unit I at (2.0,3.0,0.0) in Unit 2. This generates the same con.

figuration as shown in Fig. F11.5.7 Another way of describing this problem uses more unit descriptions. Derme the origin of the basic unit to be on the right face at the origin of the lower annulus and callit Unit 3. Define Unit I to be a hemicylindrical annulus that has its origin on the left fece. Dcfme Unit 2 to be a hemicylindrical annu-lus that has its origin on the right face. The geometry mock up for this situation is:

Fil 5.28 READ GEOhf UNIT 1 l'ifEnt/C)'L+X 011.3 2P12.0 *

(  ; 1hilC1'L+X 111.6 2Pl2.0 UNIT 2 1*llEnflCYL-X 011.3 2P12.0 l> l'IlEhflC)'L X 111.6 2P12.0

& UNIT 3

i. l'IlEhflC)'L X 011.3 2P12.C

)'llEhflC)'L X l 11.6 2P12.0 CUBOID 010.0 -2.0 2Pl2.0 8.0 -2.0 11 OLE I -2.0 0.0 3.0

\ 11 OLE 2 0.0 0.0 6.0 -

END GEOh!

READ ARRA)' NUX~l NUl'.I NUZ=1 F1LL T3 END ARRA}'

READ BOUNDS XFC=hilRROR END BOUNDS Assume that the origin of the ban.: unit is at the center of the cuboid and include the lower right 1 hemicylindrical annulus in the basic unit. Define the basic unit to be Unit 3. Define Unit I to be the heraicylindrical annulus having its origin on the left face. Define Unit 2 to be the upper hemicylindri-cal annulus. This mxk-up will be the same as the previous one except for changes required by the shift in the location of the origin.

$ READ GEOh!

UN171

)~l11 bilC)'L+X 011.3 2P12.0 l'lI'inflCYL+X ! ! 1.6 2P12.0 UNIT 2 l'HEhflC)'L-X 011.3 2P12.0 l'HEhflC)'L-X 1 1 1.6 2P12.0 UNIT 3 .

YHEMICYL-X 011.3 2P12.0 ORIGIN 1.0 -3.0 YHEhflCYL-X 111.6 2P12.0 ORIGIN 1.0 -3.0 CUBOID 012Pl.0 2P12.0 2Ph.0 HOLE 1 -1.0 0.0 0.0 HOLE 21.0 0.0 3.0 END GEOh!

READ ARRAY NUX=1 NU)'-l NUZ-1 FILL T3 END ARRAY REA D BOUNDS XFC. AllRROR END BOUNDS Define Unit I to be a hemicylindrical annuia oriented like the top and bottom ones in Fig. Fil.5.7.

Define Unit 2 to be a hemicylindrical annulus oriented like the middle one in Fig. Fil.5.7. Defbe Unit 3 to be the cuboid with the origin at its center. Use holes to place all three hemicylindrical annuli in the cuboid. Tte teometry mock-up for this situation follows:

Fl 1.5.29 R

READ GE0h!

UNITI f l'IlEnllC1'L.X 011.3 2P12.0 l'ilEhflC)*L.X 111.6 2P12.0 UNIT 2 1'llEh!ICl'L+X 011.3 2PI2.0 l'ilEhflC)'L+X 111.6 2P12.0 UNIT 3 CUBOID 012Pl.0 2P12.0 2P3.0 ,

llOLE I 1.0 0.0 3.0 llOLE I 1.0 0.0 3.0 llOLE 2.l.0 0.0 0.0 END GEOh!

READ ARRAl' NUX.I NUl'=1 NUZ=1 FILL F3 END ARRA1' READ BobNDS XTC=hilRROR END BOUNDS in the above description, the first 1101.E description places the lower annulu? at its proper location.

The second ilOLE cescription places the upper annulus at its proper. position and the third ilOLE description places the middle annulus at its correct position.

Fi1.$.6.2 Nesting lloles This section illustrates how holes are nested. Holes can be nested to any level. Consider the config-uration that was illustrated in Fig. Fil.5.6 and replace the large rods with a complicated geometric-arrangement. The resultant figure is shown in Fig. Fil.5.8.

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Fi l.5.31 Figure Fil.5.9 shows the complicated geometric arrangement that replaced the large rods of Fig. F i l .5.6.

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Fi 1.5.32 Figure I'll.5.10 shows a component of the arrangement shown in Fig. Fil.5.9.

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• x Fig. Fil.5.10. Geometric component represented by Unit 4 There is no predetermined "best way* to create a geometry mock up for a given physical system.

The user should decide the order that is most convenient. In order to describe the configuration using nested holes, Fig. Fil.5.8,it may be most convenient to start the geometry mock up at the deepest nest-ing level as shown in Fig. Fil.5.10. The small cylinders are composed of mixture 1, they are each 0.1 cm in radius and 30 cm long. There are five small cylinders used in Fig. Fil.5.10. Their centers are located at (0,0,0) for the central one, at (0,0.4,0) for the bottom one, at (.4,0,0) for the :ight one, at (0.4.0) for the top one, and at ( .4,0,0) for the left one.' The rectangular parallelepipeds (cuboids) are composed of mixture 2. Each one is 30 cm long and 0.1 cm by 0.2 cm in cross section. The large cylinder contaicing the configuration is composed of mixture 3, is 30 cm long and has a radius of 0.5 cm. The geometry mock up for this system is described as follows:

(1) define a small cylinder to be Unit 1, (2) define a small cuboid with its length in the x direction to be Unit 2, (3) define a small cuboid with its length in the y direction to be Unit 3, (4) define Unit 4 to be the large cylinder and place the cylinders and cuboids in it using holes.

i F11.5.33 UNIT 1 C1'LINDER 1 10.12P15.0 ,

UNIT 2 CUBOID 212P0.12PO.05 2P15.0 UNIT 3 CUBOID 212PO.05 2PO.! 2P15.0 UNIT 4 C1'LINDER ! l 0.12P15.0 C)*LINDER 310.5 2P15.0 llOLE ! 0.0 -0.4 0 0 flOLE I 0.4 0.0 0.0 flOLE 10.0 0.4 0.0 11 OLE 1 0.4 0.0 0.0 ll OLE 2 -0.2 0.0 0.0 llOLE 2 0.2 0.0 C ?

IlOLE 3 0.0 -0.2 0.0 llOLE 3 0.0 0.2 0.0 The first cylinder places the central rod, the first ilOLE places the bottom cylinder, the second ilOLE places the cylinder at the right, the third ilOLE places the top cylinder, the fourth flOLE places the cylinder at the left, the fifth IlOLE places the left cuboid whose length is in x, the sixth IlOLE places the right cuboid whose length is in x, the seventh IlOLE places the bottom cuboid whose length is in y, and the eighth IlOLE places the top cuboid whose length is in y.

Now that Fig. Fi1.5.10 has been described, consider Fig. Fl1.5.9. The large plain cylinders are composed of mixture I and are 0.5 cm in radius and 30 cm long. The cylindrical component of Unit 4 is the same size, an outer radius of 0.5 cm and a length of 30 cm. The small cylinders that are located in the interstices between the large cylinders are composed of mixture 2, are 0.2 cm in radius, and are -

30 cm long. Define Unit 5 to be the large plain cylinder and Unit 6 to be the small cylinder; Unit 7 is the annulus that contains the cylinders. Its origin is at its center. The annulus is composed of mixture 4, has a 1.3-cm inside radius and a 1.4-cm outer radius. The volume between the inner cylinders is -

void. The large cylinders each have a radius of.0.5 cm and are tangent, Therefore. their origins are offset from the origin of the unit by 0.7071068. This is from-x 2 7 2 ,(o,$ +0.5 2

)2 where x and y are equal. The geometry mock up for this portion of the problem follows:

UNIT 5 C1'LINDER 110.5 2P15.0 UNIT 6 C1'LINDER 210.2 2P15.0 UNIT 7 CYLINDER 210.2 2P15.0 C1'LiNDER 011.3 2P15.0 flOLE 5 0.7071068 0.0 0.0 llOLE 6 0.7071068 0.7071068 0.0 11 OLE 4 0.0 0.7071068 0.0 llOLE 6 -0.7071068 0.7071068 0.0 flOLE 5 -0.7071068 0.0 0.0 llOLE 6 -0.7071068 -0.7071068 0.0 llOLE 4 0.0 0.7071068 0.0 llOLE 6 0.7071068 -0.7071068 0.0 CYLINDER 411.4 2P15.0

Fil.5.34 In Unit 7, the first cylinder description defines the central rod and the second cyi ader defines the void volume in which the smaller cylinders are to be placed.

The first HOLE places the larger cylinder of mixture I at the right with its origin at (0.7071068,0.0,0.0),

- the second ilOLE places the small cylinder in the upper right quadrant, the third ilOLE places the top cylinder that contains the geometric component defined in Unit 4, the fourth 110LE places the small cylinder in the upper left quadrant, the fifth HOLE places the larger cylinder of mixture I at the left, the sixth HOLE places the small cylinder in the lower left quadrant, the seventh HOLE places the bottom cylinder that contains the geometric component defined in Unit 4 .

and the eighth HOLE places the small cylinder in the lower right quadrant.

The last cylinder defines the outer surface of the annulus.

To complete the geometry mock-up, enosider Fig. Fil.5.8.

Define Unit 8 to be the cylinder of mixture 2 having a radius of 0.6 cm and a length of 30 cm.

Define Unit 9 to be the central rod and the large annulus centered in a cuboid having an 8-cm-square cross r,ection and being 32 cm long.

UNIT 8 CYLINDER 210.6 2P13.0 UNIT 9 CYLINDER 210.6 2P15.0 CYLINDER 013.6 2P15 IlOLE 72.00.00.0 11 OLE 82*2.00.0 llOLE 7 0.0 2.0 0.0 IlOLE 8-2.02.00.0 llOLE 7-2.02*0.0 llOLE 8 2*-2.0 0.0 flOLE 70.0-2.00.0 110LE 8 2P2.0 0.0 -

CYLINDER 413.8 2P15.0 CUBOID 014P4.0 2P16.0 In Unit 9, the first cylinder defines the rod of mixture 2, centered in the annulus.

The second cylinder defines the void volume between the central rod and the annulus.

The first HOLE places the composite annulus of Unit 7 to the right of the central rod, the second IIOLE places a rod defined by Unit 8 in the upper right quadrant of the annulus, the third HOLE places the composite annulus of Unit 7 above the central rod, the fourth HOLE places a rod defined by Unit 8 in the upper left quadrant of the annulus, the fifth HOLE places the composite annulus of Unit 7 to the left of the central rod, the sixth HOLE places a rod defined by Unit 8 in the lower left quadrant, the seventh HOLE places the composite annulus of Unit 7 below the central rod, and the eighth HOLE places a rod defined by Unit 8 in the lower right quadrant.

The last cylinder defines the outer surface of the annulus. The outer cuboid is the last region.

Fl 1,5.35 This problem illustrates three levels of hole nesting. The total input data for the problem is given below. The nuclide ID's are for the 16-group ilansen Roach working format library. The mixtures used in this problem are not realistic or meaningful, llowever, the geometry description accurately recreates the geometry arrangement of Fig. Fil.5.8. This problem includes the data for a printer plot to be used to verify the validity of the geometry description T he plot data specify a picture that is 260 characters w'de, so the picture is generated in two pieces. The left half of the printer plot is shown in Fig. Fil.5.Il and the right half is F ven i in Fig. Fil.5.12. The user can tape the two halves together.

If the plot were specified to be 130 characters wide, it would all print in one piece. Ilowever, some of the detail mi Fht have been lost.

Fi1.5.36 NESTED HOLLS SAhlPLE READ PAR hi RUN NO LIR 41 TAIE 0.5 END PAR 4%I RE4D AllXT SCT I MIX =I 92500 4.7048 2 MIX.2 2001.0 AllX 3 502 0.1 AllX.4 2001.0 END AllXT RL4D GEOAl UNIT I CYUNDER I I 0.12 PILO UNIT 2 CUBotD 212P0.12P0.05 2 PILO UNIT 3 CURotD 212P0.05 2PO.I 2 PILO UNIT 4 CYLihDER II0.12P!LO CYLINDER 3 I 0.5 2 PILO Il0LE I A0 0.4 0.0 ll0LE I A4 0.0 0,0 ll0LE I 0.0 0.4 0.0 il0LE I .0.4 0.0 A0 ll0LE 2 -0.2 0.0 0.0 ll0LE 2 0.2 A0 0.0 Il0LE 3 0.0 -0.2 0.0 ll0LE 3 0.0 0.2 0.0 UNIT 5 C)*LINDER I 10.3 2 PILO UNIT 6 C)'LINDER 2 i A1271LO UNIT 1 CYUNDER 210.2 2 PILO -

CYUNDER 0 I l.3 2 PILO HOLE 5 A7071068 2*0.0 ll0LE 6 0.7071N8 0.7011N8 0.0 il0LE 4 0.0 0.7071N8 0.0 fl0LE 6 0.7071N8 0.7071N8 0.0 HOLE 5 -0.7071NS 0.0 0.0 HOLE 6 0.7071068 -0.7071068 A0 Il0LE 4 0.0 -0.7071N8 0.0 HULE 6 0.7071068 0.7071068 A0 CYUNDER 4 i L4 2 PILO UNIT 8 CYLINDER 2 i A6 2P!LO UNIT 9 C)'LINDER 2 i A6 2P!LO CYLINDER 0 I16 2 PILO fl0LE 7 2.0 A0 0.0 HOLE 8 2*2.0 0.0 HOLE 7 0.0 2.0 A0 HOLE 8 2.0 2.0 0.0 HOLE 7 2.0 2*A0 HOLE 8 2*.2.0 0.0 HOLE 7 A0 2.0 A0 HOLE E 2P2.0 A0

< CYUNDER 4 l 18 2PlLO CUB 0lO O I 4P4.0 2 PILO END GEOM RL4D ARMY NUX.! NUY-1 NUZ 1- TILL 9 END ARRAY READ PLOT TTL.'X.Y SLICE AT Z MIDP0lNT. NESTED HOLES' XUL. 0.1 - n1L.E.1 ZUL LLC XLR 8.I YLR 0.1 ZLR-16

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F11.5.39 Fll.5.6.3 Muhiple Arrays Section Fil.5.6 demonstrates how units are composed of geometry regions and how these units can be stacked in an array. This same procedure can be extended to create multiple arrays. Furthermore, arrays can be used as building blocks within other arrays.

Consider Sample Problem 12 from Sect. Fil.D. The description of this sample problem is restated below as Sample Problem 19.

This problem is a critical experiment consisting of a composite array u fofour highly enriched ura-nium metal cylinders and four cylindrical Plexiglas containers filled with uranyl nitrate solution. The metal units in this experiment are designated in Table 11 of ref. I as cylinder inder 11 and reflector index 1. A photograph of the experiment is given in Fig. Fil.D.3. The coordinate system is defined to bc z up the page, y across the page, and x out of the page.

The Plexiglas containers have an inside radius of 9.525 cm and an outside radius of 10.16 cm. The inside height is 17.78 cm und the outside height is 19.05 cm. Four of these containers are stacked with a center-to-center spacing of 21.75 cm in the *y" direction and 20.48 cm in the *z" direction (vertical).

This arrangement of four Plexiglas containers can be described as follows: mixture 2 is the uranyl nitrate and mixture 3 is Plexiglas, so the Plexiglas container with its appropriate spacing cuboid can be described as Unit 1. This considers the array to be bare and suspended with no supports.

UNIT 1 CYLINDER 219.525 2P8.89 CYLINDER 31 10.16 2P9.525 CUBOID 014P10.875 2P10.24 The array of four Plexiglas containers can be described as array I in the array data as follows:

A RA - 1 NUX-1 NU)'. 2 NUZ-2 FILL FI END FILL The four m:dal cylinders each have a radius of 5.748 cm and are 10.765 cm tall. They have a _

center-to-center spacing of 13.18 cm in the *y* direction and 12.45 cm in the *z" direction (vertical).

Thus, one of the metal cylinders with its appropriate spacing cuboid can be described as Unit 2. This array is also considered to be bare and unsupported.

UNIT 2 CYLINDER 1 1 5.748 2PS.3825 CUllOID 01 4P6.59 2P6.225 The array of four metal cylinders can be described as array 2 in the array data.

ARA-2 NUX=1 NUY- 2 NUZ-2 FILL F2 END FILL Now two arrays have been described. The overall dimensions of the array of Plexiglas containers is 21.75 cm in x, 43.5 cm in y, and 40.96 cm in z. The overall dimensions of the array of metal cylinders is 13.18 cm in x,26.36 cm in y, and 24.9 cm in z.

F11.5.40 In order to describe the composite array, these two arrays must be stacked together into an array, in order for them to be stacked into an array, the adjacent faces must match. This is accomplished by defining a Unit 3 which contains array 1, the array of Plexiglas solution containers. The overall dimen-sions of this unit are 43.5 cm in x and y and 40.96 cm in z. These dimensions are calculated by the code and need not be specified. Unit 3 is defined as follows:

UNIT 3 ARRA Y ! 3

• 0.0 The array of metal cylinders will be defined to be Unit 4. Ilowever, this array is smaller in the y and z dimensions than the array of Plexiglas units. Therefore, a void region must be placed around the array in those directions so Unit 4 and Unit 3 will be the same size in y and z. This is accomplished by using a reflector card as follows: _

UNIT 4 A RRA Y 2 3

• 0.0 REPLICATE O I 2*0.02*8.572*8.03i Now that Unit 3 and Unit 4 have been defined, they must be placed in the global or universe array.

This is done in the array data and the global array number is set to 3 as follows:

GBL-3 A RA -3 NUX-2 NUY. ! NUZ-1 FILL 43 END FILL This completes the geometry description for the problem. The complete input description for the prob-lem is given below. The nuclide ID's are for the 16-group Hansen Roach working format library.

l.

-- __-_____-____________m__ _ _ _ _ _ _ _ _ . _ . , , _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ , _ _ _ _ _ _ _ _ ____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ____ _ _ __

l2 F11.5.41 1

-XENos SAAIPLE PROBLEAl I9 4 AQUEDUS 4 AIETAL ARRAl' 0F ARRAl'S READ PARAAf LIB-41 RUN NO END PARAAf RL4D AtlXT SCT-1 AtlX-1 92860 3.2275 3 925014.4802-2 AllX 2 !!O2 3.812 7100 1.9733 3 8100 3.6927 2 92301 9.8471 4 92860 7.7697 5 AllX-3 6100 3.35$2 2 1102 5.6884 2 81001.42212 END AllXT RL4D GE0Af UNITI Cl'LINDER 219.5258.89 8.89 C)'LINDER 3110.16 2P9.525 CUBOID 014P10.875 2P10.24 UNIT 2 C)'LINDER I 15.748 2P5.3823 _ _ .

CUBolu 014P6.59 2P6.225 UNIT 3 ARRAl' I 3*0.0 UNIT 4 ARRAl' 2 3*0.0 REPLICATE O 12*0.02*8.572*8.031 END GE0Af READ ARRAl' ARA I NUX-1 NUl'.2 NUZ-2 TILL FI END FILL ARA 2 NUX-1 NU)'.2 NUZ-2 FILL F2 END FILL GBL-3 ARA-3 NUX-2 NUY I NUZ-1 FILL 4 3 END TILL END ARRAl' READ PLOT TTL *X l' SLICE AT Z-10.24' XUL--LO l'UL-44.5 ZUL-10.24 XLR-35.93 l'LR -LO ZLR-10.24 UAX- LO VDN - LO NAX = 130 NCil ' *..' Plc. AlIX END TTL 'X Z SLICE AT l'-10.875' XUL--l.0 l'UL 10.875 ZUL-41.96 XLR-33.931'LR IO.875 ZLR= l.0 UAX-LO WDN -l.0 PIC- AllX END END PLOT END DATA END "

A printer plot of an x-y slice taken through the bottom layer of the array is shown in Fig. Fil.5.12.

A printer plot of an x-z slice taken through the left half of the array is shown in Fig. Fil.5.13. These printer plots were used to verify the geometry rnock-up.

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• 4444 ggg * * -* .. ****'.... . . . . . . . . . 4444 44, ....e 4444 444 4 4

. d 44 4 4 4 44 4 4 4 44 4 44 d 4 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 44 44 4 4 44 4 d d 4&4 4 4 4 4 4 44 4 4 4 4 4 4 4 444 44 4 8 4 8 4 4 4 4 4 44 44 4 4444 444 444 4a44 444444 4 444444444444 4 444444d44444 4 4 4 4 4 4 4 4 44 44 4 4 4 4 44 4 444 4 444 4 444 4 4444 44d 4444 44 44 4444 44 4 44 44 444 4 88 4 4 4 4 4 4 444 4 4 4 4 4 4 4 4 d e 4 4e. J 44 4 4 44 4 44 4 8 44 4 4 44 444 4 44 4 44 4 4 4 4 4 4 4 4 d 4 44 48 4 8

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F11.5.44 ,

STORAGE ARRAY Consider a storage array of highly enriched uranium buttons, each 1 in, tall and 4 in, in diameter.

These buttons are stored on stainless steel shelves with a center-to-center spacing of 2 ft between them.

The shelves are 1/4 in, thick,18 in, wide,20 ft long, and are 18 in. from the top of a shelf to the bot-

. tom of the shelf above it. Each rack of storage shelves is four shelves high, with the first shelf being -

6 in above the floor. - The storage room is 19.5 ft in the x direction by 43 ft in the y direction with 12-ft ceilings in the z direction. The walls, ceiling, and floor are composed of concrete, it thick. All the aisles between the storage racks are 3 ft wide. The racks are arranged with their length in the y direction and an aisle between them The array of racks are arranged with two in the y direction and five in the x direction. Mixture 1 is the uranium metal, mixture 2 is the stainless steel, and mixture 3 is the concrete.

First, describe the metal button and its center-to-center spacing The void vertical spacing has arbi-trarily been chosen to extend from the bottom of the button to the next shelf above the button. The shelf of stainless steel is described under the button.

, UNITI CYLINDER I I 5.082.540.0 CUBOID 0 i 2P22.86 2P30.48 45.72 0.0 CUBotD 21 2P22.86 2P30.48 45.72 .635

< Array I creates an array of these buttons that fills one shelf. Unit 2 then contains one of the shelves i shown in Fig. Fi1.5.14.

A RA - 1 NUX- 1 NUY.10 NUZ-1 FILL F1 END TILL i

y UNIT 2 1 ARRAY l 3

• 0.0 i

i Stack four Unit 2's vertically to obtain one of the racks shown in Fig. Fil.5.14. One rack is defined by l array 2.

ARA - 2 NUX- 1 NUY~l NUZ-4 FILL F2 END FILL Generate a Unit 3 that contains a rack of shelves and a Unit 4 that is the aisle between the ends of the two racks in the y direction.

UNIT 3 ARRA Y 2 3*0.0 UNIT 4 CUBotD 01 2P22.86 2P45.72 185.42 0.0 Stack Units 3 and 4 together in the y direction to create Unit 5 which contains both racks in the y direction and the aisle between them. This is the configuration shown in Fig. Fil.5.14.

f Fi l.5.45 k

tb

\\\

\\\\ i

\\\\

\/W 9

ll\  :-

l M 0 0 3 0 l

0 0 0- 0 l-l

\/\/\/

4 Fi l.5.46 ARA-3 NUX-1 NUY-3 NUZ-1 FILL 343 END TILL UNIT $

ARRAY 3 3

• 0.0 ,

Create a Unit 6 which is an aisle 3 ft wide in the x direction and'43 ft in the y direction (full length of the room).

UNIT 6 CUB 0lO OI 91.44 0.0 1310.64 0.0 185.42 0.0 Stack Units 5 and 6 in the x direction to achieve the array of racks in the room. .Then put the 6-in.

spacing below the bottom of the racks, the spacing between the top of the top rack and the ceiling, and add the concrete floor, walls, and ceiling around the array, Array 4 describes the array of racks in the room. The core description encompasses this array, and the first reflector descriptions are used to add the spacing between the top rack and the ceiling. The last two reflector descriptions add the ceiling, walls and floor. A perspective of the room is shown in Fig. Fil.5.15.

GBL-4 ARA -4 NUX-9 NUY.I NUZ-1 FILL $ 6 3Q2 5 END FILL LORE 413*0.0 dEPLICATE O 1 4*0.0 165.1 15.24 i REPLICATE 3 2 6*3.0 6 REPLICATE 3 8 6*0.48- 1 The final mock-up for this room is given below. The printer plots for this problem must be quite large in order to see all the detail because the array is sparse and the shelves are thin. Therefore, the printer plots for this system are not included as figures. The user can generate the printer plots if it is desirable to see them. The first two plots are two pages wide and the last one is only one page wide.

The nuclide ID's used in this problem are for the 16-group ilansen Roach working format library.

9

m. _ ,._

Fil5A7

/

<\ f i / MN  !

/

- xx

\L\ e\sm\ lj \\\\

/ Q\ \

( 'NN%{x \

xx N ?x\ xx g @e4 R sygg gggyy x

x g'fh\MNgg hhter, ygy xgg x

\

sgu ifsfx/sf

Fil.5A8

-KEN 05 STORAGE ARRA1' READ PARAnfETERS ThfE-1.0 FDN YES LIB-41 END PARAnfETERS READ AllXT SCT.I hfIX-192500 4.48006 2 92800 2.6578 3 92400 4.827-4 92600 9.57 5 AllX-2 2001.0 AflXu] 3011 END AfiXT READ GEOh!ETRY UNIT 1 C1'LINDER I 15.082.540.0 CUBOID 012P22.86 2P30.48 45.72 0.0

- CUBOID 212P22.86 2P30.48 45.72 -0.635

~~

UNIT 2 A RRA l' I 3

• 0.0 UNIT 3 -

ARRA Y 2 3*0.0 UNIT 4 CUBotD 012P22.86 2P45.72185.42 0.0

- UNIT 5 ARRA Y 3 3*0.0 UNIT 6 CUBO!L) 0191.44 0.01310.64 0.0185.42 0.0 CORE 413*0.0 REPLICA TE O 1 4*0.0 165.1 15.24 i REPLICATE 3 2 6*3.0 6 REPLICATE 3 8 6*0.48 !

END GEOh!ETRY READ ARRAY ARA-1 NUX-1 NUY-10 NUZ-! FILL F1 END FILL ARA =2 NUX-1 NUY I NUZ-4 FILL F2 END FILL ARA-3 NUX=1 NUY-3 NUZ-1 FILL 3 4 3 END FILL GBL-4 ARA-4 NUX-9 NUY-1 NUZ-1 FILL 5 6 3Q2 5 END FILL END ARRAY ^

RE4D BIAS ID=3012 8 END BIAS READ START NST=4 TFX-0.0 TFY-0.0 TFZ-0.0 NBX-5 END START READ PLOT PLT NO TTL 'X-Z SLICE AT Y-30.48 WITH Z ACROSS AND X DOWN' XUL-594.8 YUL-30.48 ZUL--l.0 XLR.-0.5 YLR-30.48 ZLR-186.0 WAX = LO UDN--l.0 NAX-260 NCH * *R.' END TTL.*Y.Z SLICE OF LEFT RACKS, X 22.86 WITH Z ACROSS AND Y DOWN' XUL-22.86 YUL-1311.0 ZUL=-0.5 XLR-22.86 YLR. 3.0 ZLR-186.0 WAX l.0 VDN--1.0 NAX 260 END TTL *X-Y SLICE OF ROOh! THROUGH SHELF Z-0.3175 WITH X ACROSS AND Y DOWN' XUL--l.01TIL-1312.0 ZUL-0.3175 XLR-596.0 YLR= 2.5 ZLR=0.3175 UAX.1.0 VDN -LO NAX 130 END END PLOT END DATA END

F11.5.49 YI1.$.6 4 Arrays and floles Sections Fil.5.6.1 and 2 describe the use of holes and Sect. Fil.5.6.3 describes multiple arrays and arrays of arrays. lloles can be used to place arrays at locations that would have been impossible with earlier geometry restrictions. This section contains examples to illustrate the combined use of arrays and holes.

EXAMPLE 1. A SIMPLE CASK Consider a cylindrical mild steel container having an inside radius of 4.15 cm and a radial wall thickness of 0.45 cm. The thickness of the ends of the container is 1.27 cm and the inside height is 10.1 cm. liighly enriched uranium rods I cm in diameter and 10 cm long are banded together into square bundles of four. These bundles are then positioned in the mild steel container as shown in I ig. F i l.5.16. The rods sit on the floor of the container and have a 0.1-cm gap between their tops -

and the top of the container.

ORNL-0WG 83-10097

//YA'$$'////,,,,

/

'Y /,

//

/

/

/

// ..

/

, y

// 7,yg/// ,

Fig. F11.5.16. Uranium rods in a cylindrical container To generate the geometry description for this system, define Unit I to be one uranium rod and its associated square pitch close packed spacing region.

UNIT 1 C1'LINDER 11 0.5 2PS.0 CUB 01D 01 4P0.5 2PS.O Define array 1 to be the central square array consisting of four bundles of rods.

F11.5.50 ARA 1 NUX-4 NU)'=4 ' NUZ= l ' FILL FI END FILL _

Define array 2 to be a bundle of four rods.

. A RA = 2 NUX= 2 NbY-2 NUZ-1 FILL - El END FILL Now place array '2 in Unit 2. This defines the outer boundaries of an imaginary cuboid that contains the array. It is convenient to have the origin of the array at its center, so the most negative point of the -

array will be ( l,-1,-5).

UNIT 2 ARRA }' 2 -1.0 -1.0 -S.O A core description is used to place array 1 in the global unit. Then the cylindrical container. is described around it and holes are used to place the four outer bundles around the central array.

CORE 1 2.0 -2.0 10 C)'LINDER 01 4.15 Li -LO flOLE 2 0.0-3.00.0 llOLE 2 3.0 0.0 0.0 llOLE 2 0.0 3.0 0.0 ilOLE 2 -3.0 0.0 0 0 C1'LINDER 214.66.37-6.27 The first hole places the bottom bundle of four rods the second hole places the bundle of four rods at the right, the third hole places to top bundle of rods and the fourth hole places the left bundle of rods.

The overall problem description is shown below. Two of the printer plots used for verification of .

this mock-up are shown in Figs.- Fil.5.17 and Fil.5.18.

1 1

1 l

F i l .5.51 '

-KEN 05 CASK ARRA)*

READ PARAhfETERS ThfE-1.0 FDN.l'ES LIR-41 GEN-10 END PARAhfETERS READ hilXT SCT.I hilX.I 92500 4.48006 2 92800 2.6578 3 92400 4.827-4.

92600 9.57 5 AllX-21001.0 END hilXT RE4D GE0hlETRl' UNIT l C1'LINDER 110.5 2PS.0 CUBOID 014PO.5 2P5.0 UNIT 2 ARRA l' 2 -1.0 -1.0 -3.0 CORE I i -2.0 2.0 3.0 C1'LINDER 0 1 4.15 5.1 -5.0 ll0LE 2 0.0 -3.0 0.0 ll0LE 2 3.0 0.0 0.0 fl0LE 2 0.0 3.0 0.0 ll0LE 2 -3.0 0.0 0.0 C)'LINDER 214.66.37-6.27 END GE0h!

RL4D ARRAl' ARA.1 NUX-4 NU)'-4 NUZ-1 FILL F1 END FILL ARA-2 NUX 2 NU)'-2 NUZ-1 FILL FI END FILL END ARRAl' READ PLOT TTL 'A .' SLICE AT l' 0.25 WITH X ACROSS AND Z DOWN' XUL -5.01'UL O.25 ZUL-6.5 XLR-5.0 l'LR-0.25 ZLR=-6.5 UAX-1.0 WDN= I.0 NAX 130 NCll.' 'O' END TTL *X-l' SLICE AT Z-0.0 WITil X ACROSS AND l'DOWN' XUL=-5.0 l'UL-5.0 ZUL O.0 XLR-5.0 l'LR=-5.0 ZLR= 0.0 UAX-1.0 VDN--l.0 NAX-130 END END PLOT END DATA END s

y - y ry- y:,--- ,----m , -- e e -+,.c r--,-, 4 _ _-e,-.- ,u i -yr - ,4--u , -- -- r.. y , , - , , y t

- 1:II'S'SC 9

.................................................................................................................4.........

.. . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . . . . ......... ...................................4

......................... ... -......................... - r.

1

..............................4........................

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

) .................................................................................

u 3!83[ir 11 x-A s!!oa oj nisu! nut Jops !u a b gppoul t oouts!uaJ 1a

_ __ m . . _ -. - ______. _ _ _ _ _ . . _ _ -_. __ _ _ __ _ __

F'l 1.5.53

,,,,,,,,,o,,,,,,,,,,,,,,,,,,,,,,,,,,,,...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

,,,,,, . . . ~ . .

Fig. Fil.5.18. x-z slice of uranium rods in a cylindrical container EXAMPLE 2. A TYPICAL PWR SHIPPING CASK Consider a typical PWR shipping cask. illustrated in Fig. Fil.5.19. The interior and exterior of -

the cask is carbon steci and a depleted uranium gamma shield is present in the annulus The shipping cask contains seven PWR fuel assemblic:. Each assembly is a 17xl? array of fuel rods with water holes as shown. Each assembly is contained in stainless steel.- Each fuel rod is clad with zircalloy and is composed of 4% enriched UO3 Rods of H.C clad with stainless steel are positioned between the fuel assemblies. The entire cask is filled with water.

f., - - , , , . 9 - *- ,- .,-y, e9 #--4 - - # y , ,wm.- , ,,,,m..y,-- .-- - , , , i.-, i.+<--.-,-,,,,- w-.,4 e , , - , - -.. .. - ,,v

Fi 1.5.54 k

k, i

... s

+

w T~ G h n plh i u

pk m ,u g ,,

),<

, $.lh.w ke 3 N Mh. b.f

._t .

i ,1 ,p 3 4i n 4 4 4 g ii n, i

\

f

.6 VL '

g. ..

/y.qF . .

as . .

l'f) ' a e

.(,'%[. . .

'gi

.j e e e o e e o e e e e e e e o e e e

. . e e e .

e o e o e e

. . e .

a a e .

. . e .

O . p .

O . O .

e e e . . e e .e e . . e e . e .e o e e e e . . . . . e .

G .

D .

Q .

0 .

O O

_ a 3? ;$J&&.... .s*clV

Fig. Fil.5.19. Typical PWR shipping cask To destrh the geometry of tlic cask, start by defining some simple units as shown in Fig. Fil.5.20.

l i

-- , . . , , , - - . , . . _ . , - , , - . - . . . , . . . ~ , - - . a..._, , , , ,

F11.5.55 ORNL-DWG 8314 792 UNIT 1 UNIT 2 - UNIT 3 UNIT 4 UNIT $ UNIT G O O I?ig. Fil.5.20. Simple units Unit I represents a fuel rmi and its associated square pitch spaang region. Unit 2 represents a water hole in a fuel aswmbly.

. UNIT l C1'LINDER I I .41148 365.76 0.0 C)'LINDER 2 1 .48133 365.76 0.0 CUBolu 3 I .63734. 63754.63754. 637S4 365.76 0.0 UNIT 2 CUBolu 3 I.63754 . 63754.63754 . 63754 365.76 0.0 Units 3,4, and 6 represent the 114 C rmis with their various spacings. and Unit 5 is a water hole that is use.d in association with some of the il4 C rods.

UNIT 3 C1'LINDER 4 I .384 365.76 0.0 C)'LINDER 5 1.633 365.76 0.0 CUButD 3 I .9912 . 9912 2.2352 1.27 365.76 0.0 UNIT 4 C1'LINDER 4 I .384 365.76 0.0 C)'LINDER $ 1.635 363.76 0.0 CUBOID - 3 I .9912 . 9912 1.2702 -1.235 365.76 0.0 UNIT 3-CUBulu 3 I.9912 ,9912 1.7526 1.7526 365,76 0.0 UNIT 6 C1't.INDER 4 I .584 365.76 0,0.

C1'LINDER S I .635 365.76 0.0 CUBotD 311.1875213 -1.1873215 L883706 -1.883706 363,76 0.0

- ,s , -,----w-4.--, -,_y .c , y..

l F11.5.56 Units 1 and 2 are stacked together into array 1 te form the array of fuel pins and water holes in a fuel  !

auembly as s' >wn in Fig. Fil.5.21. This array is then encompassed with a layer of water and a layer of stainless steel to complete a fuel assembly (Unit 7) as shown in Fig. Fil.5.22.

ilRA-l NUX-17 NU)'-17 NUZa l TILL 39R: 2 203 SRI 2 9R12 22R12 403 28RI 2 403 Q3122RI 2 Ql0 Q9 2Q3 39RI ENDflLL UNIT 7 ARRA)' I -10.83R18 10.83818 0.0 CUBulD 3 I Il.!!2495 11.112495 11.112495 11.112495 365.76 0.0 CUBUID 8 I 11.302238 11.302238 !!.302238 l!.3C2238 365.76 0.0 ,

l ORN L-DWG 6314793 )

l ARRAY 1 20 0000000 2 0 0 0 0 0 0 0 0 00 00000 2 0 0 0 0 000 .

2 0 0 0 0 00 0 0 OO OO OO ~

) O'O O O O O O O

) OOO O O O O O nin, _ n n .

n n i

Fig. Fil.5.21. Quarter section of fuel pin array iy .m,, ,-- ,, . - . , , , - .,,..,w,, -

,,,%y,,,-. ,w - ww- -. ,,,-, ..w,. v. 3-m-,-, yw-. y

Fil.5.57 ORNI.-DWG 8314794 UNIT 7 2 00000 0 00 2 0 0 0 0 0 0 00  :

OO 00 0 00 -

2 0 0 0 0 0 00 2 0 0 0 0 0 0 00 OO OO OO 2 00000000 2 0 0 0 0 0 0 0 0

. nn. n n .nn i

Fig. Fil.5.22. Quarter section of fuel assernbly.

An array of Unit 6's is created to represent the atiny of II.C rods that is positioned octween the fuel assernblies. This array of it4 C rods is contained en Unit 8 as shown in l'ig. Fil.5.23.

A M - 2 NUX 2 NUl'. 6 NUZ- 1 FILL F6 ENDFILL UNIT 8 ARMl' 2 0 0 0 The next step is to create the central array of three fuel assemblics with 11 4C rods between them.

This is done by stacking fuel assemblics (Unit 7) and thC rod arrays (Unit 8) into an array (array 3) and placing it in a unit (Unit 9). The resultant geometry is shown in Fig. Fil.5.24.

AM-3 NUX 3 NU)'-l NUZ-1 T*LL 7 8 7 8 7 END FILL UNIT 9 ARMl' 3 0 0 0 v

r

4 l

' Fl 1.5.58 ORNL-DWG B314800 UNil 8 (ARR AY 2) 1 OO

- l O!O OO OO OO 1 l

OO Fig. Fil.5.23. 2 x 6 array of B C 4 rods.

ORNL-DWG 8314801 UNIT 9 A

[ UNIT 7 UNIT 8

'c

^

p OO O-O OO OO OO OO OO OO i OO OO OO OO O0 00 x_

fig. Fl!.5.24. Central arrey 2ME n--T - ' '-

3- y.myege -=e set--. .---74..-c m, 7 m-g,..,4f.

. - ___ _ . _ _ _ _ _ ._ . _ _ _ _ _ _ . . _ _ _ _ _ _ . _ . _ _ . . _ _ _ _ _ _ . _ . ____m __

h Fil.5.59 Units 3,4. and 5 are used to define the arrays of B.C rods that fit above and below the central array as shown in Fig. Fil.5.25.

ARA 4 NUX-39 NU)'.I NUZ-l flLL 3 $ 202 3 4 202 5 4 3 202 5 3 202 3 4 3 202 3 202 3 END TILL UNIT 10 ARRAl'4 0 0 0 ARA-3 END TILLNUX-39 NU)'-l NUZ-1 TILL 4 5 202 4 3 202 3 3 4 202 3 4 3 202 5 3 4 202 5 2Q .i UNITII ARRAl'3 0 0 0 ,

ORNL-DWG 8314802 UNIT 10 (ARRAY 4)

O O! O 0 0 0 00 0 0g00 O 000000 C O OlO C' O O O O 1

UNIT 11 (ARRAY 5)

O 00000 00 g000 000000 O,

l0 0 0 0 0 00 0 O O O Fig. Fil.5.25. Long B.C rod arrays.

Units 9,10, and 11 are stacked to form the central array with B4 C rods as shown in Fig. Fil.5.26.

ARA -6 NUX= 1 NU)'.3 NUZ 1 FILL 119 10 END FILL-This completes the three central fuel assemblies and all 4 the B C rods associated with them. Next, Units 7 and B are stacked together to form the array of two fuel assemblies separated 4 by B C rods as shown in Fig. F11.5,27. This is designated as array 7 and Unit 12. The origin of Unit 12 is specified at the center z-27,94 cm. of the array in the x and y directions and the bottom of the fuel assemblies are at ARA - 7 NUX-3 NU)'. ) NUZ-1 FILL 7 5 7 END flLL UNIT I2 ARRAl' 7 24.979519 11.302238 27.94

F11.5.60 ORN L-DWG 83-14803 j i

ARRAY 6 l O O _

O 000000 000000 0C0000 0 0 0lglO 0 C' .O' Q OO OO OO OO OO OO OO OO OO OC OO OO OO OO 6 O O 0 0 0 0 0 0. 009090 q0 0 0 O! 000 00 O O Ol t

Fig. F11.5.26. Central array with long II.C arrays ORNL-DWG 83-14804 UNIT 12 (ARRAY 7) 00 00 00  ;

oO OO OO Fig. Fil.5.27. Two fuel assembi en and ll.C rods Unit 13 is simply a cylindrical lid that fits on top of the shwing cask. It is described relative to the origin of the shipping cask and is made of depleted uranium.

UNIT 13 CYLINDER 6 1 47.625 457.2 449.58

.The shipping cask is completed by specifying the origin of array 6 (see Fig. Fil.5.26) to be at the center of the array in x and y and the bottom of the array is at r-27.94 cm. . Note that the three dimensions specified when an ARRAY is placed in a unit are the coordinates of the most negative point in the array with respect to the origin of the unit that contains the array A cylinder of water defining the' interior of the shipping cask is described around the array. A HOLE is used to place a Unit 12 (Fig. Fil.5.27) below the array and a second ilOLE is used to place another Unit 12 above the array.

Then a cylinder of steel is placed around the water, which is in turn encased by depleted uranium. The

Fil.$.61

• depleted uranium is then contained in the outer steel cylinder of the shipping cask. A third ilOLE is used to place the depleted uranium lid (Unit 13) on the shipping cask. This completes the shipping cask description of Fig. Fl1.5.19.

ARRAl' 6 38.6368 14.807438 27.94 C1'LINDER 3 1 47.625 447.04 16.51 Il0LE 12 0.0 26.1097 0.0 ll0LE 12 0.0 26.1097 0.0 C1'LINDER 7 1 48.893 447.04 13.333 Ch'LINDER 61 $9,06 447.04 3.81 C1'LINDER 7 1 63.01 462.28 0.0 Il0LE 13 0.0 0.0 0.0 Atray 6 is the global array for this problem and is therefore not preceded by a unit definition. It defines the coordinate system for the overall problem. The geometry data for this shipping cask are stiown below. The plot data have been included for verification of the geometry description llowever ' .i the plot generated by this data is quite large and is therefore not included in this document.

r

)

5 5

1 4

+

't!

b a .. . _ . ~ , _.

, ._ .. - . . _ . - - .._,r . . _ , . . _ . . . . . . . , . ....a.,

L Fl 1.5.62 RMU GLOM UNITI C)LINDER 11.41148 J65.76 WO C)LINDER 2 I .48I33 365.76 0 0 CUBulD 3 I.63734 . 63134.63734 63134 365.76 0.0 UNIT 2 CUBolu 3 I .63134. 63754.63754. 63734 36L76 WO UNIT 3 C1LINDER 4 I .S$4 365.76 0.0 C)LINDER S 1.635 36L76 WO CUBotD 31.9912 9912 2.2352.l.27 365.76 WO UNIT 4 CYLINDER 4 I .384 365.76 0.0 C)LINDER 3 I .633 365.76 WO CUbulD 3 I .9912. 99121.2702 2.233 36L76 0.0 UNIT $

CUBotD 3 I .9912. 99121.7316.l.7326 36L76 WO UNil 6 C1LINDER 4 I .584 36L76 0.0 C)'LINDER $ I .635 36L76 0.0 CUBolU 3 I l.1873215.l.1R732151.883706 l.883706 36L76 0.0 UNIT 7 ARMY I .80.83818 lW83818 W0 CUBotD 3111.112493 1 Lil249511.112495 11.112493 36L76 0.0 CUBolu 8 I 11.302238.Il.30223811.302238 11.302238 3CL76 0.0 UNITS ARMY 2 0 0 0 UNIT 9 ARR4Y 3 0 0 0 UNIT 10 ARMY 4 0 0 0 UNIT 11 ARMY $ 0 0 0 UNIT 12 ARR4Y 7 24.979519 Il 102238 27.94 UNITI1 C)'LINDER 6 1 47.623 451.2 449.38 ARMY 6 38.6568 14.807438 27.94 CYLINDER 3 I 47.623 447.0416.31 Il0LE 12 0.0 2L1097 WO Il0LE I2 0.0 26.L497 0.0 C)LINDER 7148.893 447.04 IL333 CYLINDER 6 1 39.06 447.04 3.81 CYLINDER 7 I 63.01462.28 0.0 Il0LE IJ 0.00.00.0 END GEOM RE4D ARM Y AM e l NUX.17 NUY.11 NUZ.I flLL 39RI 2 2Q3 SRI 2 9RI 2 22RI 2 4Q3 3 SRI 2 403 Q$122RI 2 Q10 Qt 2Q3 39RI END flLL AM.2 NUX.2 NUh6 NUZel FILL F6 END flLL AM 3 NUX.5 NUY 1 NUZel flLL 7 8 7 8 7 END flLL AM 4 NUX.39 NUY I NUZel flLL 3 3 2Q2 3 4 202 3 4 3 202 3 3 4 2Q2 5432Q232Q23 END FILL AM.3 NUX 39 NUY.I NUZel flLL 4 5 202 4 3 2Q2 $ 3 4 202 3 4 3 202 3 3 4 202 3 2Q2 4 END flLL AM.6 NUX=1 NUY 3 NUZ.1 flLL 119 10 END FILL AM 7 NUX 3 NUY.1 NUZel FILL 7 8 7 ENDflLL END ARMY RMD PLOT TTL 7 SillPPING CASK 17 300 X.Y SLICE I XUL. 631TL 63 ZUL.180 XLR 631'LR 63 ZLRol80 UAX.I VDN..I NAX.330 PLT =NO END PLOT l

l

1 111.5.63 l'il.5 6.5 Sycification of the Global System KliNO peometry data must be correlated to an absolute coordinate system. In the past, the code w as responsible for determining this coordinate system KidNO V.a allows the user to define the abso-lute untdinate system by specifying the global unit. If the user does not exercise (nis option, the code udl assiFn the default as before The use of the word GLOllAL in the Feometry region data is used to speufy the global unit. A global array is required only when a problem consists of a bare array and thus has no global unit. In that event, the user can specify the global array by entering Gill- in the arra) data.

In the geometry reFi on data for a problem, the word GLOllAL preceding a UNIT NUMilliR DL1INillON or an ARRAY PLACEMENT DESCRIPTION specifies that unit to be the global unit. Only one global specification should be used in a problem. If GLOllAL is entered more than once in the geometry region data, the last entry defines the global system. The specification of a global _

umt, whether manually or by default, overrides the manual specification of the Fl obal array in the array data. EnterinF the word GLOllAL in the geometry region data always overrides the use of Gill in the arra) data.

11) default, the global unit is defined to be the last ARRAY PLACEMENT DESCRIPTION that doc. not immediately follow a UNIT NUMilliR DEIINITION. The associated surrounding geometry, if arv, is the external renector. The default global array is the array referenced by the F lobal unit or, in thi absence of a global unit, the largest array number specified in the array data. If an array is referci ced by the global unit, it is always the first geometry region in the Fl obal unit (i.e., an ARRAY PLACEMI NT DESCRIPTION is the first Feometry region in that unit.) The array number of the APRAY PLACEMENT DESCRIPTION specifies the array that is contained in the unit. This array may contain other arrays, nested to any level flowever, the global array is the one that is considered to be n the gl@al unit, just as each subsequent array within the global array is considered to be within the unit that coruins it. If the global array specified in the array data (Gill-) is inconsistent with the specifica' ion of the global array in the geometry region data, an error message will be written and the problern sill not run Some examples of global specifkation follow.

EXAMPLE 1. Consider the 2x2x2 array of sample problem I shown in Fig. Fil.D.I. The array consists of 'our identical units in each of two layers. The geometry for this problem is listed below. Ily -

default, the global array is array 1. The most neFative point of the array is located at the origin so the array extends from x=0.0 to x-27.48, y-0.0 to y-27.48 and r=0.0 to z-26.02.

SAbfPLE PROBLEhi ! CASE 2C8 BARE READ GEOAICTRl' C)'LINDER I 1 S.748 S.3823 S.3825 CUBOID 0 1 6.87 -6.87 6.87 -6.87 6.303 -6.505 END GE0AfETRl' REA D A RRA )' NUX- 2 NU)'- 2 NUZ - 2 END A RRA )'

EXAMPLE 2, Case 1. Consider the 2x2x2 reflected array of sample problem 3 shown in Fig Fil.D.2. The array consists of four identical units in each of two layers. The array is reflected by 15.?4 cm of paraffin. The geometry foi tl.is problem is listed below. By default, the global unit is the unit whose first Feometry region is CORE. Note that the array number following the word CORE is defaulted to I if a zero is entered. Array 1 is contained within this unit and is thus the global array.

In this Feometry description, the most negative point of array 1 is located at ( 23.48.-23.48,22.75) rela-tive to the origin of the global unit. Thus the array extends from x--23.48 to x- + 23.48, y- 23.48 to y - + 23 48, and z--22.75 to 2- + 22.75. The overall system extends from x 38 72 to x- + 38.72, y--38.72 to y- + 38.72 and z--37.99 to z- + 37.99.

i

l l

Fil.5.64 SAhlPLE PROBLEh! 3 2C8 l$.24 Chi PARAFFIN REFL RE4D ARRA)'NUX= 2 NU)'-2 NUZ-2 END ARRA)'

RETD GE0h!

C)'LINDER I i 5.748 5.3825.$.3825 CUBotD 0 1 11.74 .II.74 11.74 .!!.74 11.375 -11.375 CORE O ! .23.48 23.48 22.75 CUBOID 2 2 26.48 -26.48 26.48 26.48 25.75 25.75 CUButD 2 3 29.48 -29.48 29.48 29.48 28.75 28.75 CUB 0lO 2 4 32.48 32.48 32.48 32.48 31.75 -31.75 CUBolD 2 5 35.48 -33.48 33.48 33.48 34.75 34.75 CUbulD 2 6 38.72 38.72 38.72 38.72 37.99 37.99 END GEOh!

EXAMPLE 2, Case 2. The 2x2x2 reflected array of sample problem 3 above could also have been described by explicitly specifying the global unit as shown below. The geometry remains unchanged and the results will be identical. A third method would be to omit the ' UNIT 2.* Again th. geometry and results will be unchanged.

SAhlPLE PROBLEAf 3 2C8 l$.24 CAf PARAFFIN REFL READ ARRAl'NUX-2 NUY 2 NUZ.2 END ARRAY '

READ GE0hi C)'LINDER I I 5.748 5.3825.$.3825 CUBotD 01 II.74 11.74 !!.74 11.7411.373 !!.373 GLOBAL UNIT 2 CORE O 1 23.48 23.48 22.75 CUBOID 2 2 26.48 26.48 26.48 -26.48 25.75 25.75 CUBotD 2 3 29.48 29.48 29.48 29.48 28,75 28.75 CUBolu 2 4 32.48 -32.48 32.48 32.48 31.73 31.75 CUBotD 2 5 35.48 35.48 35.48 35.48 34.75 -34.75 CUB 01D 2 6 38.72 -38.72 38.72 38.72 37.99 37.99 END GE0bl tiXAMPLE 3. Case 1. Consider sample problem 15 illustrated in Fig. Fil.D.6. This problem '

requires the use of two different units to describe the Ecometry. Unit I describes the portion of the sphere that extends into the Plexiglas collar, the Plexiglas wilar and a cuboid of water tight fitting around them. Unit 2 describes the portion of the rphere that is above the Plexiglas collar, surrounded by a cuboid of water having an edge dimension the same as the diameter of the Plexiglas collar and a height equal to the partial sphere. Ther.c two units are stacked with Unit 2 on top of Unit 1. The global unit is the geometry external to the array (the CORE, CYLINDER and REPLICATE), The global unit is cylindrical in shape and has its origin at the center of the array (0,0,0). The most nega-tive point in the array is positioned at ( 12.7,12.7 7.092175). Thus the array extends from x- 12.7 to

x. + 12.7, y 12.7 to y- + 12.7, and z =.7.092175 to z. + 7.092175.

, , - - - - . - , - - . _ m . ..r=, re m--- *- -'- =n - -- - ,- -

i--vw --- - **= v v * --

Fil.5.65 SA AfPLE PROBLEAf 15 ShiALL WA TER REFLECTED SPilERE ON PLEXIGIAS COLLAR READ GE0Af UNIT 1 IIEhflSPilE.Z l ! 6.$$37 Cll0RD .$.09066 C1'LINDER 314.1273.$.09066 7.63065 C)'LINDER 2 l 12.7 .$.09066 -7.63063 CUBolD 314P12.7 $.09066 -7.63063 UNIT 2 HEAllSPilE+ Z l 16.S$37 Cil0RD 5.09066 CUBulD 314PI2.7 6.$$37.$.09066 CORE O I 12.7 12.7 -7.092175 Ch'LINDER 3117.97 2P7.0V22 REPLICA TE 3 2 3*3.0 $

END GE0Af RC40 ARRAl'NUX= 1 NU)' I NUZ-2 FILL I 2 END ARRAl' EXAMPLE 3, Case 2. Consider sample problem 15 described above. Again define Unit I to con-tain the portion of the sphere that extends into the Plexiglas collar, the Plexiglas collar and a cuboid of water snugly surrounding them. Unit 2 contains the portion of the sphere that is above the Plexiglas collar. surrounded by a cuboid of water having an edge dimension equal to the diameter of the Plexiglas collar and a height equal to the partial sphere. These two units are stacked with Unit 2 on top of Unit

1. The global unit is the geometry external to the array (the CORE. CYLINDER and REPLICATE).

The global unit is cylindrical in shape and has its origin at the center of the sphere (0,0.0). The most negative point in the array is positioned at ( 12.7.12.7,-7.63065). Thus the array extends from x- 12.7.

to x - + 12.7, y--12.7 to y- + 12.7, and z-.7.63065 to z- + 6.5537.

SA AfPLE PROBLEAf 13 SAfALL WATER REFLECTED SPilERE ON PLEXIGIAS COLLAR RC4DGE0Af UNITI 1/EAllSfilE Z l 16.5537 CHORD .$.09066 Cl'LINDER 314.1273 .$.09066 -7.63065 C)'LINDER 2112.7 $ 09066 7.63065 CUBolD 314P12.7 -$.09066 7.63065 UNIT 2 1/EAllSPflE+ Z l ! 6.$$37 Cil0RD $.09066 CUB 0lD 314P12.7 6.$$37 $.09066 CORE O I .12.7 -12.7 -7.6306$

Cl'LINDER 31 17.97 6.5537 -7.6306$

REPLICATE 3 2 3*3.0 $

END GE0Af READ ARR4l'NUX.I NU)' 1 NUZ-2 FILL 12 END ARRAl' EXAMPLE 3 Case 3. Consider sample problem 15 as described above. The problem geometry ca'n remain basically unchanged except the global unit is explicitly specified as shown below. The problem is identical to that of EXAMPLE 3, Case 2. and the results will be identical. The same problem could be run by omitting the " UNIT 3* and/or replacing

• CORE 0* with ' ARRAY 1.*

Fil.$.66 S4hlPLE PROBLEh! 13 ShfALL WATER REFLECTED SrilERE ON PLEX 1GUS COLLAR t READ GE0h!

UNIT 1 IIEhflSPHE.Z l ! 6.5537 CHORD .$.09066 C)'LINDER 3 1 4.1275 3.09066 7,63065 C)'LINDER 2112.7 .$.09066 7.63065 CUBotD 314Pl2.7.$ 09066 7.63065 UNIT 2 HEhflSPHE+ Z l ! 6.5337 CHORD 5.09066 CUBotD 314P12.7 6.$$37.$.09066 GLUML UNIT 3 CORE o I .12.7 12.7 7.63065 C1'LINDER 3117.97 6.$$37 7.63063 REPLICATE 3 2 3*3.0 $

END GEO*i READ ARRA)'NUX.I NU)*-1 NUZ 2 TILL 12 END ARRA)'

EXAMPLE 4. Case 1. Consider sample problem 19, illustrated in Fig. Fil.D.3. The array of arrays geometry for this problem is shown below. Unit I defines a Plexiglas cylinder filled with uranyl nitrate solution. Unit 2 defines a uranium metal cylinder. Array I defines the 2x2 array of solution units at the back of the figure. Array 2 defines the 2x2 array of metal units at the front of the figure.

Unit 3 contains array 1, and Unit 4 contains array 2. The global array is defined to be array 3 by speci.

fying GBL.3 in the ARRAY DATA. Array 3 is composed of Unit 3 and Unit 4 and defines the over.

all system. The most negative point in the global array is at the origin of the global unit. The global array extends from x=0.0 to x.34.93, y-0.0 to y-43.$, z.n.0 to r=46.96. This is also the overall dimensions of the implied global array.

SAh!PLE PROBLEh! l9 4 AQUEOUS 4 hiETAL ARRAl' OT ARMl'S READ GE0h!

UNIT 1 C)'LINDER 219.5258.89 8.89 C)'LINDER 3110.16 2P9.$23 CUBOID 014P10.873 2P10.24 UNIT 2 C1'LINDER I i 5.748 2PS.3825 CUB 01D & 14?6.39 2P6.225 UNIT 3 ARRA l' 13*0.0 UNIT 4 ARRA)* 2 3*0.0 REFLECTOR 012*0.02*8.572*8.031 END GE0h!

READ ARRAl' ARA =1 NUX-1 NUl'.2 NUZ=2 FILL T1 END TILL ARA-2 NUX-1 NU)'.2 NUZ 2 FILL T2 END FILL GBL-3 ARA =3 NUX 2 NU)'-l NUZ 1 FILL 4 3 END FILL END ARRA)'

EXAMPLE 4. Case 2, Sampic problem 19 could also have been described by omitting GBL-3.

The global array would have defaulted to array 3 because it is the largest array number in the array data.

lil 1.5.67 LX AMPLE 4. Case 3. Still another way of r,pceifying the data for sample problem 19 would be to omit Gill 3 in the array data and specify array 3 as the global array in the geometry data as shown below. The problem would still be identical to the previous descriptions although the geometry is speci-fied in a slightly dift: rent manner.

SA AfPLC PROHLEAf 19 4 AQUEUUS 4 AIETAL ARRAl' OF ARRA)'S READ GEUAl UNIT l C)'LINDER 2 I 9.325 8.89 8.89 C1'LINDER 3110.16 2PV.523 CUBOID 014Plu.87$ 2Plu.24 UNIT 2 C1'I.INDER I I L748 2PL3823 CUBUID 0141'6.39 2P6.225 UNIT 3 A RRA l' I 3

• 0.0 UNIT 4 ARRA l' 2 3*0.0 REILECTOR 012*0.02*8.572*8.03i GLOML A RRA )' 3 3

• 0.0 END GEUAf READ ARRA)' ARA-1 NUX-! NU)' 2 NUZ-2 FILL F1 L'ND FILL ARA =2 NUX-I NU)'-2 NUZ.2 flLL F2 END FILL ARA-3 NUX-2 NU)'.! NUZ-1 FILL 4 3 END FILL END ARRAl' EXAMPLE 4, Case 4. Consider the data specified in EXAMPLE 4, Case 1. It is possible to spec-ify a partion of that data to be the global unit. This causes the code to ignore all of the data that are not referenced by the global unit. The 2x2 array of uranyl nitrate units can be run by specifying Unit 3 to be the global unit as shown below. Only the 2x2 array of solution units will be utillred by the problem.

SAhtPLE PROBLEAf 19 4 AQUEOUS 4 AIETAL ARRA)'Of ARRA)'S READ GEUAf UNIT!

Cl'LINDER 219.52$ 8.89 8.89 C1'LINDER 3110.16 2P9.525 CUBolD 014Pl0.875 2P10.24 UNIT 2 C)'LINDER I I $.748 2PS.3825 CUBotD 014P6.39 2P6.223 GLOBAL UNIT 3 ARRA l' 13*O O UNIT 4 ARRAl' 2 3*0.0 REFLECTOR 012*0.02*8.372*8.03i ARRAl' 3 3*0.0 END GEDAf RUD ARRAl' AM = 1 NUX-I NU)'-2 NUZ~ 2 FILL El END FILL ARA-2 NUX I NU)' 2 NUZ-2 FILL F2 END FILL ARA =3 NUX.2 NU)'-I NUZ.I FILL 4 3 END FILL END ARRAl' i

Fil.$.68 EXAMPLE 4, Case 5, The prob!cm of EXAMPLE 4, Case 4 can also be specified by omitting the UNIT 3 card and placing the global specification before ARRAY I as shown below.

MAIPLE PROBLEAf 19 4 AQUEOUS 4 AIETAL ARRAl'Of ARRAl'S READ GEUAf UNIT l C)'LINDER 219.5258.89 8.89 C1'LINDER 3110.16 2P9.525 CUBotD 014P10.875 2P10.24 UNIT 2 Cl'LINDER I I 5.748 2PS.3825 CUBolu 014P6.39 2P6.225 GLOBAL A RRA l' 13 *0.0 UNIT 4 ARRA)' 2 3*0.0 REFLECTOR 012*0.02*8.372*8.031 A RRA )* 3 3

• 0.0 END GEDAt READ ARRAl' ARA.I NUX-I NUl'.2 NUZ=2 FILL T1 END TILL ARA-2 NUX-1 NU)'.2 NUZ.2 FILL T2 END TILL ARA =3 NUX.2 NU)'-l NUZ-1 TILL 4 3 END TILL END ARRAl' linth case 5 and case 4 of EXAMPLE 4 are equivalent to the following teometry data.

SAAfPLE PROBLEAl 19 4 AQUEOUS 4 AIETAL ARRAl'0F ARRA)'S READ GE0Al UNIT l C)'LINDER 219.5238.89 8.89 C)'LINDER 3110.16 2P9.525 CUBolD 014P10.875 2PIO.24 END GE0Af RE4D ARRA)* ARA

• I NUX-1 NU)'.2 NUZ-2 FILL TI END TILL END ARRA)'

I i

l Fil.5.69 i l

1 l

EXAntPLE 4, Case 6. If it is desirable to determine the keff of one of the uranyl nitrate units of ,

sample problem 19, simply specify the unit as the global system as shown below.

SAAIPLE PROBLEAf 19 4 AQULOUS 4 AIETAL ARMl'0F ARRAl'S READ GEUAf ,

GLOML UNITI a C)'LINDER 219.5238.89 8.89 C)*LINDER 3110.16 2P9.$25 CUBOID 014P10.875 2Pl0.24 UNIT 2 C)*LINDER I I $.748 2P3.3825 CUBOID 014P6.59 2P6.225 UNIT 3 ARRA)* I 3*0.0 UNIT 4 ARM Y 2 3*0.0 RETLECTOR 012*0.02*8.572*8.03i ARM)* 3 3*0.0 END GE0Af RE4D ARRA1' AM I NUX-1 NU)' 2 NUZ.2 TILL TI END TILL AM-2 NUX I NUY 2 Nl1Z-2 FILL T2 END TILL AM-3 NUX-2 NU)'=1 NUZ=1 FILL 4 3 END TILL END ARRAl' Case 6 of EXAMPLE 4 is equivalent to the data shown below.

SAhlPLE PROBLEh! 19 4 AQUEOUS 4 AIETAL ARRAl'0F ARRAl'S READ GEUAf C)'LINDER 219.5238.89 8.89 Cl'LINDER 3110.16 2P9.52$

CUBotD 014P10.875 2P10.24 END GE0Af F11.5.7 ALTERNATIVE SAMPLE PROBLEM MOCK-UPS The geometry data for KENO V can often be described correctly in several ways. Some alternative geometry descriptions are given here ^or sample problem 12 and sample problem 13. . (See Sect. Fil.D.)

F11.5.1.1 Sample Problem i2, First AIIernatIve This mock-up maintains the same overall unit dimensions that were used in sample proble'n 12. In sample problem 12, the origin of Unit 1, the solution cylirider, is at the center of.the unit; the origin of Units 2, 3, and 4, the metal cylinders, are at the center of the cylinders. In this mock up, the unit numbers remain the same and the origin of each unD : the center of the unit. In each unit the cyl.

inder is offset by specifying the position of its centerline attive to the origm of the unit.

.. - .. ~ . . _ _ _ . - - _ . _ - - _ _ . . _ - - - _.

F t 1.$.70 l

READ GE0Af UNIT 1 C)'LINDER 219.5258.89 8.89 C)'LINDER 3 1 10.16 9.523 9.525 .

CUBotD 0 1 10.875 10.875 10.875 10.8/5 10.24 10.24 UNIT 2 .

C)'LINDER 11 S.748 9.3973 1.3975 ORIS 4.285 4.285 CUBUID 0 1 10.875 10.875 10.875 10.875 10.24 10.24 UNIT 3 i C)'LINDER 115.748 9.3973 L3673 ORIG 4.285 4.285 CUBOID 0 1 10.873 10.875 10.873 10.875 10.24 10.24 UNIT 4 C1'LINDER 115.748 f.3675 9.3973 URIG 4.285 4.285 CUBolu 0 1 10.873 -10.875 10.873 10.875 10.24 10.24 UNIT $

C1'LINDER I I S.7481.3675 9.3975 ORIG 4.285 4.285 CUBolu 0 1 10.875 10.875 10.875 10.875 10.24 10.24 END GE0h!

READ ARRA>' NUX 2 NU)'.2 NUZ-2 FILL 21314 I $ 1 END ARRA)'

.-.~. .,

l 1 11.5.7 l 1:1l.S.1,2 Sampsle Problem 12. Second Alternath'r in this mock-up, the outer boundaries of the system are made as close fitting as possible on all six faces. The origin of each unit is located at the center of the cylinder. Units I,3,5, and 7 contain the metal cylinders Units 2,4. 6, and 8 contain the solution cylinders.

REA D GE ' *-1 UNIT 1 C)*LINDER I I 5.748 3.3825 .$.3825 CUBulh 0 1 6.59 3.748 6.59 14.445 6.225 13.54 UNIT 2 C1'LINDER 219.5258.89 8.89 C1'LINDER 3 1 10.16 9.323 9.525 CUB 010 0 1 10.16 50.875 10.873 -10.16 10.24 9.323 UNIT 3 C)*LINDER I I 5.748 3.3825 $.3823 CUBotD 016.59 -$.74814.444 6.39 6.225 13.34 UNIT 4 C)*LINDER 2 I 9.323 8.89 -8.89 C)'LINDER 3 1 10.16 9.525 9.525 CUBotD 0 I 10.16 10.873 10.16 10.875 10.24 -9.325 UNIT $

C)'LINDER I i 3.748 5.3825 -$.3825 CUBotD 016.59.$.748 6.59 14.44513.54 6.22$

UNIT 6 C)'LINDER 2 1 9.523 8.89 -8.89 C1'LINDER 3 1 10.16 9.323 9.525 CUBotD 0 1 10.16 10.875 10.873 10.16 9.525 10.24 UNIT 7 C1'LINDER I I 5.748 5.3825 $.3825 CUBOID 016.39 -$.74814.445 6.5913.34 6.225 UNIT 8 -

CYLINDER 219.5238.89 8.89 C)'LINDER 3 1 10.I6 9.525 9.525 CUB 01D 0110.16 -10.87510.16 10.875 9.52$ .10.24 READ ARRAl' NUX-2 NU)'-2 NUZ-2 FILL 6118 END FILL END ARRAY

_ ~ . _ _ . . _ _ _ . _ _ _ _ _ _ _ _ _ . _ _ . _ . _ _ . _ _ . . _ _ _ _ _ . . _ . _ . ._ . _ _ -. __ . . . . _

t Fil.$.72 Yll.$.1.3 Sample Problem 13. Alternative i

This mock up maintains the same overall unit dimensions that were used in sample problem 13, Sect. Fil.D. In sample problem 13, the origin of Units I,2, and 3 is located at the center of the base  :

of the uranium metal cuboid. In this mock up, the origin of Units I and 2 is located at the center of the cylinder. In Unit 3 the origin is at the center of the unit. ,

READ GEUAf UNIT 1 CUBolu !l 0.2566 12.4434 6.33 6.35 3.81 -3.81 C1'LINDER 0113.973.81 3.81 C1'LINDER ! I 19.0$ 3.81 3.81 CUB 01D 01 I9.05.I9.05 I9.05.I9.05 3.8I .3.81 UNIT 2 CUBOID 1112.4434 0.2566 6.3$ 6.33 4.28 4.28 C)'LINDER 0113.974.28 4.28 C)'LINDER I i 19.05 4.28 4.28 CUBotD 0119.0$ 19.0319.03 19.03 4.28 4.28 UNIT 3 CUBotD 1 1 12.4434 0.2366 6.33 6.33 1.308 -1.308 CUBotD 0 I l9.05 -19.0$ 19.03 -19.0$ 1.308 -1.308 END GEOM READ ARRA)' NUX-l NU)'ml NUZ-3 TILL I 2 3 END ARRA)'

1 i

F11.5.73 l l

Fil.5.N tilASING OH WElGilTING DATA l

Section I 11.2.3 discusses the basis of weighting or biasing. The use of biarang data in renected problems has been illustrated in Examples 9,10, and 11 of Sect. Fil.5.6. Section Fil.4.7 discusses the input directions for entering biasing data. ,

I lacry peometry card requires a bias ID to associate that geometry region with a biasing or weight. *

, ing function. A biasmg or wei Fhting function is a set of energy. dependent values of the average weight that are applicable in a given region. The default function for all bias ID's is constant through all energy groups and is defined to be the default value of weight average which can be specified in the parameter data A bias ID can be associated with a biasing function, other than default, by specifying it in the biasing input data. This function can be chosen from the weighting library or can be input from cards- Table Fil.4.5 lists the materials and energy group structures for biasing functions avail.

able f rom the weighting library.

In general. the use of biasing should be restricted to external renectors unless the user has generated (orrect biasing functions for other applications. Improper use of biasing functions can result in errone-ous answers without giving any indication that they are invalid Caution should be exercised in the gen.

eration and use of biasing functions.

liiasing functions are most applicable to thick external reflectors. Their use can significantly reduce the amount of computer time required to obtain answers in KENO V. If the user wishes to use a bias-ing function for a concrete reDector, for example, the following steps must be included in preparing the input data:

O The geometry region data must define the shape and dimensions of the tenector using the mix.

ture ID for concrete and a sequence of bias ID's that asseciate the geometry region with the appropriate interval of the concrete weighting function. CAUTION: TiiE TillCKNESS OF EACil REGION UTILIZING lilASING FUNCTIONS MUST MATC11 OR VERY

' NEARLY MATC11 T11E INCREMENT TillCKNESS OF Tile WElGIITING DATA.

NO CilECK IS MADE ON TIIE REQUIREMENT. IT IS Tile USER'S RESPONSIBile ITY TO ASSURE CONSISTENCY.

(2) liiasing data must be entered. This must include the material ID for the reflector material (from Table Fil.4.5 or as specified on cards) and a beginning and ending bias ID. The begin-ning bias ID is used to select the first set of energy dependent average weights, and the subse-quent sets of energy-dependent average weights are assigned consecutive ID's until the ending bias ID is reached.

Small deviations in reflector region thickness are allowed, such as using three generated regions with a thickness per region of 5.08 cm to generate a 15.24 cm thick reDector of concrete, or using five gen.

crated regions with a thickness per region of 3.048 cm to generate a 15.24 cm thick reflector of water.

See Table Fil A.5 for a list of the increment thickness for each material in the weighting library, it is acceptable for the thickness of the last rencetor region to be significantly different than the increment i

thickness. For example, a renector card specifying five generated regions with a thicknesss per region-of 3.0 cm could be followed by a reficctor card specifying one region with a thickness per region of 0.24 cm. Assume material 2 is water and a 15.24-cm-thick cuboidal renector of water is desired. The required reflector description and biasing data could be entered as follows:

REFLECTOR 226*3.0 5 RETLECTOR 276*0.241 READ BIAS ID=500 2 7 END BlAS

- - - - _ - v..-.re.--<-e+ ,..~4, ,.. y,---w . _ 3, .y , _ - ..,---s- ,-ms + , -

.-c- - - +.. a.e-#, , mw.-%

Fl 1,5.74 The same 15.24 cm thick reflector can be described by including the extra 0.24 cm in the last region as shown below:

RETLECTOR 226*3.0 4 REFLECTOR 266*3,24I RC4D BIAS ID-500 2 6 END BIAS liere the weighting functions associated with bias ID's 2,3,4, and $ are defined by the first reflec-tor card and each generated region has a thickness of 3.0 cm, corresponding exactly to the increment thickness for water in Table Fil 4.5.11ias ID 6 is used for the last generated region which is 3.24 cm thick.

The following examples illustrate the use of biasing data. Suppose the user wishes to use the weighting function for water from Table Fil.4.5 for bias ID's 2 through 6. The biasing input data would then be:

READ BIAS JD 500 2 6 END BIAS The energy-dependent values of weight average for the first 3 cm interval of water will be used for weighting the geometry regions that specify a bias of ID of 2. The energy-dependent values of weight average for the second 3-cm interval of water will be used for geometry regions that specify a bias ID of 3, etc. Thus, the energy-dependent values of weight average for the fifth 3-cm interval of water will be used for geometry regions that specify a bias ID of 6. Geometry regions that use bias ID's other than 2,3,4,5, and 6 will use the default value of weight average that is co.istant for all energies as a biasing function.

Several sets of biasing data can be entered at once. Assume the user wishes to use the weighting function for concrete from Table Fil.4.5 for bias ID's 2 through 4 and the weighting function for water for bias ID's 5 through 7. The appropriate input data block is:

RE4D BIAS ID=3012 4 ID-500 5 7 END BIAS The energy-dependent values of weight average for the first 5-cm interval of concrete will be used for the geometry regions that specify a bias ID of 2, the energy dependent values of weight average for ,

the second 5-cm interval of concrete will be used for the geometry regions that specify a bias ID of 3, and the energy dependent values of weight average for the third 5-cm interval of concrete will be used for the geometry regions that specify a bias ID of 4. The energy-dependent values of weight average for the first 3 cm interval of water will be used for geometry regions that specify a bias ID of 5, the values for the second 3-cm interval of water will be used fcr geometry regions that specify a bias ID of 6, and the values for the third 3-cm interval of water will be used for geometry regions that specify a bias ID of 7. The default value of weight average will be used for all bias ID's outside the range of 2 through 7.

If the biasing data block defines the same bias ID more than once, the value that is entered last supersedes previous entries. Assume the following data block is entered.

READ BlAS ID=400 2 7 ID.$00 $ 7 END BIAS Then the data for paraffin (ID-400) will be used for bias ID's 2,3, and 4, and the data for water (ID-500) will be used for bias ID's 5,6, and 7.

EXAMPLE 1. Use of biasing data with a reflector card,

r e

Fil.5.75 l

Assume a 5-cm radius sphere of material 2 is reficcted by a 20-cm thickness of material 1 (con.

cretc). The concrete reficctor is spherical and close fitting upon the sphere of material 2. The mixing table must specify material I and material 2. Material I rnust be defined as concrete, Tbc geometry and biasing data should be entered as follows:

READ GEUAf SPilERE 215.0 REPLICA TE I 2 3.0 4 END GEUAf 1 READ BIAS ID 3012 5 END RIAS in the above example, the replicate card will generate four spherical geometry regions, each 5.0 cm thick. The bias ID for the first generated region is 2; the second, 3; the third, 4; and the fourth, 5.

The biasing data block specifies that the biasing function for material ID 301 (concrete) will be used from the weighting library. The bias ID to which the energy-dependent weighting function for the first 5.0-cm interval of concrete is applied is 2; the energy-dependent weighting function for the fourth 5 cm interval of concrete is applied to the fourth generated geometry region. This generated region has a bias ID of 5.

Example I can be described without using a reflector card as shown below. The cards that are gen-erated by the reflector card in the previous set of data are identical to the last four spheres in this moc k-u p.

EXAMPLE 1. Use of biasing without a reficcior card.

READ GE0h!

SPflERE 213.0 SPHERE I 210.0 SPHERE I 315.0 SPHERE I 4 20.0 SPHERE I $ 23.0 END GE0h!

READ RIAS ID=3012 $ END RIAS Fil.5.9 PRINTER PLOIS Printer plots are generated only if a plot data block has been entered for the problem and PLT =NO has not been entered in the parameter data or the plot data. When a printer plot is to be made, the user MUST correctly specify the upper left hand corner of the plot with respect to the origin of the plot. The origin of a plot is defined as follows:

(1) SINGLE UNIT The origin of the plot coincides with the origin of the geometry description.

(2) UNREFLECTED ARRAY This is an array problem that does not have a CORE or ARRAY-description in the EXTENDED GEOMETRY DESCRIPTION of the global array. The origin of the plot is located at the most negative point of the global array. This occurs at the lower left hand back corner of the global array.

(3) REFLECTED ARRAY - The origin of the plc,t coincides with the origin-of the CORE or ARRAY description in the EXTENDED GEOMETRY DESCRIPTION of the global array.

_. _ _ ~ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . .. _ _ __.__ _ _ _ - _ _ _

Fi l.5.76 i

Printer plots can represent mixture numbers, unit numbers or bias ID numbers. A title can be entered for each plot. If plot titles are omitted, the title of the KENO case will be printed for each plot title until a plot title is entered. If a plot title is entered and a subsequent plot title is omitted, the last

plot title prior to the omitted one wdl be used for the omitted one.

The upper left and lower right coordinates define the area (i.e., the slice and its location) for which the plot a to be made. The direction cosines across the page and the direction cosines down the page define the direction of the vector across the page and the vector down the page with respect to the geometry coordinate system. One of the simplest ways of generating a plot is to specify the desired coordinates of the upper left and lower right corners of the plot. Determine which plot axis is to be across the paFe and which is to be down. The sign of the direction cosine should be consistent with the direction of that component when moving from the upper left to lower right corner. For example, to draw a plot of an x r slice at y-5.0 with x across the page and z down the page for a system whose x coordinates ranFes from 0.0 to 10.0 and whose z coordinates range from 0.0 to 20.0, the upper left coor.

dinate could be XUL-0.0 YUL 5.0 ZUL-20.0 and the lower right coordinates could be X LR - 10.0 Y LR - 5.0 ZLR -0.0. Since x is to be plotted acioss the page with x-0.0 at the left and x-10.0 at the right, only the x component of the direction cosines across the page need be entered. It should be positive because going from 0.0 to 10.0 is moving in the positive direction. Thus, UAX 1.0 would be entered for the direction cosines across the page. VAX and WAX could be omitted. Z is to be plotted down the page with z 20.0 at the top and z-0.0 at the bottom. Therefore, only the z com-ponent of the direction cosines down the page need to be defined. It should be negative because moving from 20.0 to 0.0 is moving in the negatise direction. Thus, WDN=.I.0 would be entered for the direc-tion cosines down the page. UDN and VDN could be omitted. The sign of the direction cosines should be consistent with the coordinates of the upper left and lower right corners in order to get a plot.

I It is not necessary that the plot be made for a slice orthogonal to one of the axes. Plots can be made of slices cut at any desired angle, but the user should exercise caution and be well aware of the distortion of shapes that can be introduced. (Nonorthogonal slices through cylinders plot as ellipses.)

The user can specify the horizontal and vertical spacing between points on the plot. It is usually advisable to enter one or the other. Entering both of them can cause distortion of the plot. DLX- is used to specify the horizontal spacing between points and DLD- is used to specify the vertical spacing between points. When only one of them is specified, the code calculates the correct value of the other such that the plot will not be distorted. The spacing for an undistorted plot is defined as DLD*LPI-DLX* CPI where LPI is the number of lines per inch printed vertically and CPI is the num.

her of characters per inch horizontally. These parameters are a function of the printer or print chain.

The vertical distortion factor, VDIS, is then defined by VDIS (DLD*LPI)/(DLX' CPI). The code then calculates the number of intervals that will be printed across the page and down the page if both the upper left and lower right coordinates of the plot were entered. In some instances, it can be desir.

able to distort a plot by entering both DLX and DLD. It might be desirable to compress one dimension relative to another. If DLX-0.5 and DLD-5.0 are entered as data for a printer that prints 10 charac-ters per inch across and 8 lines per inch down, the portion of the plot that is printed in the vertical-direction will be reduced by a factor of 8 relative to the portion printed in the horizontal dimetion

(( 5.0' 8 )/(0.5' 10)). - That is, if the coordinates specify a perfect square, the plot will be a rectangle that -

is about 8 times as wide as it is tall.

DLX or DLD can be specified by the user to be small enough to show the desirable detail in the plot. - The plot is generated by starting at the upper left corner of the plot and generating a point every DLX across the page; then moving down DLD and repeating the generation of the points across the l l

page.

l

Fl 1.5.77 NAX specifies the number of intervals that will be printed across the page. It may be convenient for the user to specify the number of characters that can be printed across the page on the printer that will be used. Larger plots can be created by specifying multiples of this number. In that case, the plot snust be taped;together to see the overall plot. The plot will print one page wide and full length. Then the next page pidth and full length will be printed, etc., until the entire plot is completed.

NDN specilies the numb- of intervals that will be printed down the page. If both NAX and NDN are entered. the plot may be distorted. If one of them is entered, the value of the other will be calcu.

lated so the plot will not be distorted.

LPI, the number of lines per inch that are printed on a page, can be entered to be consistent with the printer that will be used The default value is 8 Imes per inch. This parameter need be entered only once for a problem. It should be entered in the data for the first plot so all the plots will be ponted in the same manner.

When a plot is being made, the first character represents the coordinates of the upper left cornet.

The value of DELV is added to the coordinate that is to be printed across the page and the next char.

acter is printed. DELY is added to that value to determine the location of the next character. That is, a point is determined every DELV across the page and a character is printed for each point. When a line has been completed, a new line is beFun DELU from the first line. This procedure is repeated until the plot is complete. Some examples of printer plots are shown in Sects. Fil.5.6.1, Fil,5.6.2. Fil.5.6.3 and Fil.5.6.4. Further examples are shown below.

EXAMPLE 1. SINGLE UNIT WITil CENTERED ORIGIN Consider two concentric cylinders in a cuboid. The inner cylinder is 5.2 cm in diameter. The outer cylinder has an inside diameter of 7.2 cm and an outside diameter of 7.6 cm. 13oth cylinders are 30 cm high. They are contained in a tight fitting box whose wall thickness is 0.5 cm and whose top and bottom are each 1.0 cm thick The inner cylinder is composed of mixture 1, the outer cylinder is made of mixture 4, and the box is made of mixture 2. The problem can be described with its origin at the center of the inner cylinder. The problem description for this arrangement is shown below:

- KENOS SINGLE UNIT CONCENTRIC C)*LINDERS IN CUBotD WITil ORIGIN A T CENTER READ PARAhl RUN NO LIB-41 ThfE-0.5 END PARAhi READ AllXT SCT-1 AflX-l 92500 4.7048 2 kilX=2 2001.0 AflX=3 302 0.1 h!!X=4 2001.0 END hilXT READ GE0h!

C)'LINDER I I 2.6 2Pl$.0 C1'LINDER 013.6 2P15.0 C1'LINDER 413.8 2Pl$.0 CUBotD 014P3.8 2P13.0 CUBotD 214P4.3 2P16.0 END GE0h!

l READ PLOT TTL.*X.)' SLICE AT Z AllDPOINT, SINGLE UNIT CONCENTRIC CYLS.*

XUL. 4.6 l'UL.4.6 ZUL.O.0 XLR.4.6 YLR=-4.6 ZLR= 0.0 UAX-1.0 VDN l.0 NAX= 130 NCil= * * .X' END PIC-UNIT NCil 'Ol' END END PLOT END DATA END l

l-

~

~ - - . -. -

Fi l.5.78

t The plot data block included above is set up to draw a mixture map of an x y slice taken at the half i height (ze0.0) and a unit map for the same slice. The code will print question marks for points outside -

the range of the problem geometry description. 11y setting the plot dimensions slightly larger than the  ;

geometry dimernions, a border of question marks will be printed around the specified plot. This verifies that the outer boundaries of the geometry are contained within the plot dimensions, in the above exam-plc, the geometry dimensions extend from x--4.3 to x-4.3, from y- 4.3 to y-4.3, and from z. 8.0 to z 8.0, An x-y slice is to be printed at the half height (z 0.0). The desired plot data sets the upper left hand corner of the plot to bc x--4.6 and y-4.6. The lower right hand corner of the plot is speci-fied as x 4.6 and y- 4.6. These data are entered by specifying the upper left hand corner as XUL -4.6 YUL 4.6 ZUL 0.0 and the lower right hand corner as XLR-4.6 YLR- 4.6 ZLR-0.0. It is desired to print x across the page and y down the paFe. Therefore, the x direction cosine is specified across the paFe,in the direction from x- 4.6 to x=4.6 as UAX-1.0. The y direction cosine is specified down the page, from y-4.6 to y- 4.6 as VDN. l.0. It was desirable for the plot to be one page wide (130 characters) so the number of characters across the page was specified as NAX-130. An arbitrary '

choice was made to print a blank for a void, a

• for mixture 1, a - for mixture 2, and a , for mixture 4.  :

Mixture 3 was not used in the problem, so a character did not have to be entered for it in the character ,

string. Thus, a character string of NCli.' *. ' would have been sufficient but a string of NCil * ' .x' I was entered. Since only three mixtures were used, only the first four characters were utilized. The blank represents a void, the

• represents the smallest mixture number used in the problem (mixture 1), .

the represents the next smallest mixture number used in the geometry description (mixture 2) and the represents the largest mixture number used in the geometry (mixture 4). The resultant printer plot and associated data are shown in Figs. Fil.5.28 and Fil.5.29. A second printer plot covering the same area shows a unit map rather than a mixture map. This unit map and associated data are shown in Figs. F11.5.30 and Fi1.5.31.

....m........ . m. .. . .m u no .

• ,JC  !=;,0!L

' ' !JC.,

..:"" +

. . . . . . . . . m............ m...........

Fig. Fil.5.28. Associated data for single unit mixture map ligure Fil.5.31 shows a block'of l's surrounded by a border of ?'s. This indicates that the entire slice-specified in the plot data was part of Unit 1. For this problem the entire volume is Unit 1.

- - - . - - - . . . . . . - - . - . - - . , - . - . . . ~,-c- - -, -.. - , . - - - . - .,, -- - ,, ,

&llTL6 g g a g g.e ... . . . . . ............*..................gggg g g g g g . . . ........*4..... ... ..... .. . . .. .. .. .. ......... .. .. .. .. .. .. . . . .. .. .. .. . .............................................gg.3 ggg g.. . . . - . .... .....,.,.............,.,..,...........................................on . .. . . . . g g g

.g...**

.......... 3

. ....*.. . . 43

.....a--*

'**.~*....

.........3

. . . .. . ... . .. . ... . .. . ... ... . ... ... . .. . ... . .. . ... . .. . ... ... . .. . ... . .. . ... . .. . ... .. . . . . . . . . . ...- ... ..e. . ......... . . . . . . . . . . . . .

U 8' dIITt6 W!xinJ med oj siu3ga nu!t pty asuta2ap op3 !u

.....u....... . . .. - n m. .

ii .

. ....e.... ..

.. a. .>.r..I . . .

..=..... .

d!8jitygo yssopetop pete joJ stu$ at nu!t nun med

1 1:11.5.8f)

..,.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,4,4,..,t,,,,,

.., .................89,,,,0,,t,1,11,...,.,.,,,,,t.t.,,it.,,.,,,,,,,,,,,,9,,tt4,,,t.et.t,,,,t,,,t,,0,

.. .. t ,,,,,, , it.,,,. . ....,t ,, ,,,0,,

,,,,,1,,,i,,,,t.e,t,,..,.t,.,,,t,',1

,, ,4t99 t9 09, t ,,,,,,,,,,0.. ... ,,,,1.

9 4 9 ,,1,,,, ,,,

,,,,,,,t,,,5,,,,,i,0,d,.,,,4,,,,,,,,t.,,t.,,991,,,,,,4,1,,90,,,44,,,a,,,1,9,,,,,,,,1,.,,,1,4,,,,1,.,,,1,,,,,,,1,.,,,,,,0,,4.,,,,,,,,,,,,,,,,,,,,,,,,,.,.,.,.,t.,,,

, ,,,,,,4,,,,n , ,t, ,,,,,, ,,,,,,,,,,t.,, ,,,,,t... 4, ,,,,, ,4 ,,,,,, 9,,,,,t.. ,, , ,

,,,p.,..,.t,1,,,,,,,,,t....,g,,,e.,,,,,,,,,,,,,,,,,,,,,,,,t.,4,,4,,,1,.....,..,,,ti,,,,tti,tt.,1,tt,44,,1,,.,119,,0,,,,,,,,,,,,,,,,,,,

,,,,,,t,,t,..,..,,1,4,.0,1,9,,,,,t.t.,.,..,e,t.,.t,0,,,,,,,e,,tl.,0,,,tt,,,8,t,.,,,,,t....tt..,

t t , 9 ,1, 0 . 0 , , t , , ,,1,,,,

..,9,,,,.

9 ,1. t. t , 8 , , , , ,..,,t...1,,,,,,,,tte,,,9,1,,,,,,,,,,,

,,9 ,1,. ,t,,,,,,,,,,,,,, t

,,,,,, ,4, , ,,, ,,,

,,,,,,,,,t..,,,,,9,,,0,,,,=,0,,,,0.,99,91,1,,,,

, , , , , , , , , , , , , , , , , ,,,,,,,,I.,,18,,11,,,,,,,,4,1,,,4,,,,,,,,,,,111.1,1.,1,9.,1,,1,,9,,,,,,,,8tt,,i,,,,,1,.,,,,,,,,,,

,t.,,1,,,tt.,,t,ti,,,,,,,.,t...tt,.t,.,. ,,4gt,1.,,,t,,,,,,,,,,9,e...ttt.n,,,

,,,,,1.,,t,9,I,t,,t....,6,1,,4,,1,5t,,,,,,,,tl,,,titt,,,,,,,,,t,4,,,,, ,,,,4

,,,,,,,,,11...,,,,,,1,,.,I.,,t..I.,,

t4...,1,,,,,

,,,,..,1,41,11,,,,1,1,,1,,,!,,,,,0.,,s,,,,t,,4,1,9,4,,,,,,,,19.,,,,,,,,1....,..,....,,,,,,,4,,,t,,..,,,,,

, ,,,, ,, ,,,,,8..... t 4

,,,, ,,,,,....,=t ,,,,,. .t. 0 ,,94,,,,,,t,,,, , , ,,,

,,,,,,0,...

n,,tt,i,,,9,,,,,,,

,,,,,,,,,,,n.9,n.9,8,,,,,,,,,,,,,,,,1,0,,,,0,,,0,,,,4,,,,,,,0.,...,,.,1,.....t.,ii,...,...,...,,,0,,4,,,t..,,9,..,,,,,

,,,,,1,,1,,1,1,l.,1,,1,, ,,,-, ,, , ,os .t.,,,,,,, s...lt. ,9,, ,t..,0,, ,, ,,0.n...., t., n ,, ,,,,,q,,n , ,,,,

,,,,,,,,,,,,,,,,,s.,t,.,0t,,,,,,,,,,,,,,,1,,,,,,.

,,,,,,,,,,,,,,,,eq,, ,,,t,,e.,ti,,t,.,,t,,t.,,,,91,t,.,...,,,,1,.,,...,.,,,,,,t.,,,ltt,,,,,,,,,,,,,,99,,,,9,,,t,.,.,.t.,,,,,,,,,,,,,,,,,,,,,,e,,,,,,t,,,4,,tt,,,,,

t,tt,,, , ,ttt,tt,t 1,t4,,t,,t.....,,,t,1.,,,t,,, ,t 4,,,,, ,

t,,,,,,

,,,,,,,t,,t;,,,,,4,,,,,,,,It.,.t,,,,,,,,,,t,,,,,,,,4,,,1,.,,,,,,,

,,,,t... ,,,,,t.,,,0..t..,,, ,, ,9,t,,,,tt

,,,t,,,,,,t,,,l,,,1,,.,.,,,,,,,,,,,,,,,,,t,,1,,,,

,,,,,t,,t,,,,,,,,t,...,.,.,..,..946t,,9,,,,,,,,1,.,..,,

, , , , , , , , ,,t,,,,

,,,,, , ,1 ,1

,,,,=,,1,,,t,,,tt,,,1, t,,,

t

, t ,; t, ,c

,1,, 1,

%,,,,,0.t1,68,1,...,.,..,,4,,,,,,I...,1.8,,,,,t,,4,,1,t,t,0,,,,,t.,,14,,9,,,,,

,,,,0..,,,,,,8, ,,,,,,,,,

t,,,,,

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t,,4.,

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. ., . ,, . , . t,

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,,,tt

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nn g g t ,1, ,1 1, ,1,1,1, ,,t,5,,,,,,,,, , , , , , , ,

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,,,, ,15 1

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,,,9,, ,,,1,5, ,9tt,9 t, i t0 tt tot,1911

. S t , tt itt ,4 t t tttt tt.ttttt t, t i t t ni t,,,ttot t t i t t t i t. t t i l i i t t t,9 9 4 t 9 9 619119 9 9 9t 9i 9 t n9t4f 415 l o , 9t 9,, t ,,i t tn, ,t nn ti tn int414, , t tn n liit ttt ,i,11111 t t,, t t ,, n , t tt tst tt ,,, t t t t t t t t t t t t, t t t i e t t t t t t t t t t, t t t t t t ,t t t t t

, ,, ,, t, , i,t nnt t ,i t, 4tt tt t,6,t t tst.,0.t i,1,11 t 14 t 19,1111111114 tettonits, ,, t i t t 0 i,l,4 4,9 t 1,4tstot 4 t 19141119,14 tnit In5 q l,t 911t nt 1,1,111111,41 n n, n I,t t t ot 11,11 t t n ti f 11111,14t n t tt t t, t t tn ttt tt t t ttt tin t t t tn t ,,,,

t t t t t t t t t t t t t t t, t, t t, t t t t t, g 14,9,,,,,

,9,,,,4

, ,,, t t li4ttt 9t i9,414 t li t i t90181516 t919 t t t 9t i9ti 9t t9t 9t t9t 9 t t 9t ti9 t91419 t t t i t t9t ti tt t19 ti t911191414t t t t t t i 14 t ei tt tt e a t t6t tti tt tl tt t,t il119 i t tt ill ill t19 e t t9i 9t t9t910t t l 6e 6t tt g19t ;; 9 t5t5t 4t t414 t t t 9t tt 11416 I t ei t tt $%t % t t% t t 1t tt tt tt tt tt tt tt ,,,,

t t t t t t t t t e t ,,,,

,,9,,14 t 1819 9 9 9 9181014 9 9 9 9 9 614 6 B (19 4 414 61119 4 0 4 4 4 9111910 41151111t i t t t ill t t t i t i t t e lli t t t t t t t t t t t t t t t t t t t t t i t t t t t t t t t t t t t t t t t t t t ,,,,

,,,9,, e t t t t t t ; $ l t a t t t t l e i t t t t t t t t t t t t t t t t t t t t t t t t t t t i t t t i t i t t t t t t t t t t t , t t t t t t t t i t t0411999.,.,,,

.,9,,,9,,19119 4 416 4 t t 9 9 9 9 9 9 91616 4 4 9 419t i t t t t t t t t t t t t t t i t t t t t t t t illi t t t t t t t t li t e t t t t titttt t t t t il n t t t t t t t t,i t t,i t ttttttttttt, nlittlntq ilt qtttttttttttttttttittittittttttttt

, f,,,,

, ,,, t 19n51115 e e9

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e911111114 t n t i4 910 n t4 i,9 9 t9 9t 9t9t9 9t 9o9 9o9110 o 9t 4o9 9,9 t91114 t e819 t ,9 $ ltitttttttnt,to,t 9 918 9 5 6 t t t tt tt t t t t t t t t titi t t t l ,,,

t i t t e li t t i t t t t t t t t t i ti t t i t t t t t l4 9 4 0 4 9 9110 % t 91119 4 t 111. ,,,

,,,t,,, toOtttttttts,,,1

,,, t 8 5 4 911115ttt $ t 411,919, titot,n,11410 4 9 9 9 9 9, t t , , n ,1, ,119 4 4,41,91

• t 111,116 4119 415 9 9191414 410 t 41119 9 9n ,, , n , t , , t t t t t t t t t t t t t t 9,,,, ,4, t t , t t ,1, t t e , , t t t t t , , ,1, t t t t , t , , t o , n 41, 5 4 t t t t t t t t t t t t t t 9 9 9 t i t t 19 4

• t t t t t t t t t t t t t t t t t t t t t t t t t t t t t ,t t t t ti t t t t t t t t t t t t t t t t t t t t t t t t l e t t t t t t t t t t t t t t t t t t % i t e t t i t t t t t ,,,,

,,9,9,1115

,, ,, 8114 9 9 9 4 t 19 4 9 514 4 9 9 9 411019 81 t t t t t t ti t t t t t t t t t t t t t 16 t t t t t t t t1511101199911919tl%t199991999919999999f t t t t t t t l e t t l1 tit tt t e t t g,,,

,,,,,4 t i t t t t t t t ll t il t t t t t t t t t t t t t t i t t t t t t t t t t t11 t i t t t i t t li t e t i t t t t t t t t t t t t t t t tilit t t t t t t t t t t tliit t t t t t t t t t t t t t t t t t t t t t t t t t t t t s ,,,

,,,,,t

,,,,,tit ttt 19 t ist t etie tt t tt tlit t tt ttt ttt tt t tt ttt ttt tt t tt tei t tlit ttt ttt l19 i t t t t ttt itt t ttt til t ttt tl ett te19t t4 4t 4t 4t9t9 t9 t9 9t 9t 9t9t6 tt tt9 tt ttt tlit ttt te19t9e5 t ti ttt ttt ttt tt il116 t t tt ttt ttt tt t tt ttt ttt tt t t19t 9t9t t... tttttttttttttttttttttttttti

,,,,,19 9 4 8 t 4 91419 0 t 9 9 9 619 4,110 f I t t6t4t 419 t ill e t t t t t t t t t t t t t t t t t t t t t 9 4 t 9 91119 9 9 4114 91101 t 9 4111919 9 9 4t t i t t t t t t t t t t t t t t t i t t t t t t t t t16 t t t i.

,,,,,4114914949999,991161919

,,,,,4 9 9 9 9 4 4 t 14 9 t t 9 9 9 4 9 914 4 4 4 9 9 9 9 9 9 9 9 9 9 9 9 4 9 9 9 9 4 4 4 4 516 6 9 9 9 9 9 9 9 6 0 911619 t 14 9119 9 9 4 6 6 619 .., 9 % 9191911119 9 9 9 9 9 9 9 9 9 9119 9 91 %14

,,,,,t it t t t t t t t t t lli t t t t t t t t t t t t t t t t t s t itit t t t t t t ti s t e llit t t t t t t t tit t t t t lt t t t t t t t t t t t t t tit t t t t t t t9119 9 9 419119 4 t t 9191919 9 9 91114,,,,

,,,,,i t t g lii t t t t i t t i t t t t t t t t t i t999991199991110119141111191t 1119 t t t t t t t t t t t i t t t t t t ti t t t t t t t t t t t t9 9 % 915 9 9 91115 4 41 E 919 9 6 4 419 4 6119...,

,,,,,t t it tillt t t t t t t t t t t t t t e lit tfi t el t t t tt t t tt t t t t t t t t tiltit t t t t t t t t t t t t t t t t t t t t t t t t tilltitt t t t t t t19 9119 9 9 9 911191 t 141119 919119,,,,

,,,,,t i t t t t t t t t t t t t t ill e t t t e lli t t ti t t t t t t t t t t t t i t i t t t t t t t t t t t t t t t t t t t i t t t t t t t t t ti s til t t t t t t t t t ill191111115 t 19 4 t I10115 4 419 91119,,,,

,,,,,111111196111 ti t t t t tit t t t t t t t t t t t t t t tit t s, titqt19

$ t t t t t t t t t t t 19 ti t t t t t t t t t t t illit t i t t l e t t t t9t 6 t ttt 15e l 6e 9t t4114t t t t t4t 919149 419 t 169 51181111111115 9999995999 9 9111414111111111116t 914 4 tit t t t t t ttiliit t tli t ttttttt ttt tt tt tt tt tt ttttt tt ttt titt tt tt ttt...t t...,

9,,,,,

, ,,,, t, s,, t ,i ,,,,t t, t ,,,,

t t,t t t t,t t,l ,,,e,,t ,t t ,, ,t t ,t,t t,,t

, ,I t ,,,,, ,t t t,,t t ,,,,,,

i .t i ,t t ,t ,t t ,,, t t t t,,t ,,, ,t t ,t t t,, t t t, t t,,t t t t ,t t ,,

,,,,,,,,, t t t,,,

,,* 1, ,,t t,,,,,,

,t t t t t t t,, t t t,,,,,t t t t,,e ,, ,l,,,,,i t t ,t ,t t ,,l i ,,,,, t t t t t ,t t t ,t t t t t t, t i t, t t t li, t i, t t,l e,,,

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,0,,,,,,,,,,,,,,,,,,,,,,,,4,,,,,,0,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

I~ig. Fil.5.31. Unit rnap printer plot for single unit with centered origin

1 l

Fil.5 91 liXAMPLl! 2. SINGLE UNIT WITil OFISET ORIGIN The physical problem is the same as that described in Example 1, two concentric cylinders in a cuboid. The dimensions are exactly the same. The difference is in the choice of the origin. In this geometry description, the origin was specified as the most negative point of the unit, the lower left back corner. Thus, the cylinders have to have an origin specified to center them in the cuboid and the cuboid .

c:tends from 0.0 to 8.6 in x and y and from 0.0 to 32 in z as shown in the problem description below. )

-KENO $ l SINGLE UNIT CONCENTRIC C)'LINDERS IN CUBulD WITH ORIGIN AT CORNLR

)

READ l' ARA AI RUN.No LIR 41 TAIE.0.5 END l' ARA Al RI:AD hilXT SCT.I AllX.! 92500 4.7048 2 AllX.2 2001.0 AllX-3 $02 0.1 AllX.4 2001,0 END AflXT READ GEUAl  !

CI'LINDER I i 2.6 31.0 LO ORIGIN 4.3 4.3 \

CYLINDER 013.6 31,01.0 ORIGIN 4.3 4.3

)

CYLINDER 413.8 31.01.0 ORIGIN 4.3 4.3 CUBOID 018.10.38.10.531.01.0 l

CUBulD 218.60.08.60.032.00.0 1:ND GLOAf '

READ PLOT 1TL.'X.Y SLICE AT Z AllDi'0 INT. SINGLE UNIT CONCENTRIC CYLS.*

XUL. 0.3 YUL-8.9 ZULO 16.0 XLR 8.9 l'LR 0.3 ZLN.16.0 UAX-I.0 l'DN..!.0 NAX.I30 NCH ' *..X* END l Plc. UNIT NCH. 'Ol' END 'l i

END l' LOT END DA TA END The plot data included above will draw a mixturc map of an x.y slice taken at the half height (r 16.0). It will also draw a unit map of the same slice. The plot dimensions extend 0.3 cm beyond the problem dimensions to provide a border of question marks around the plot. The associated plot data specification for -the mixture map is shown in Fig. Fil.5.32, the mixture map _is_ shown in Fig. Fil.5.33, and the associated plot data for the unit map is shown in Fig. Fil.5.34. The unit map is identical to Fig. Fil.5.31 and is not included. Note that Fig. Fil.5.33 is identical to Fig. F11.5.29.

....uc...... ... ..m. n . a m. .

...~.u.

l:::: .":! ll-" ';;;

'::::::: t!!::::::

!." ' -  !.!'l:.

i""

. . . .... .6.. ,,,....., . . . , . . . . . . .

Fig. Fil.5.32. Associated data for mixture map of single unit with offset origin

-,--y-,, # e. ...#.- , - -,, ,m_.9 ,y.....y,- , - myy -.,---_7__- - - - , _ , w n w. ..-.- , , _ _ _ - . p_ -...7- - -- -r,... , - , - - - < - , , ,.w,.- . - -

1:1 l'S'SE

.................................................................. ........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . t

. . . . .. ... .. ... .. ... .. ... .. ..... ..... ..... ........................ .. ... .. ..... . . . . . . . . . . . .l >

...............................................=........

..p.....-...... ... . . .. . ... ..

. - ...-- . . . . . ................gg.

.. ... .. .. . . . . . . . * . . . * . + . + - . . * . . . . . . . . + . . . . . . . . . . . . . .

• * * * * * * * * * * * * * * *****=************.**=.************.***s*=*.*=*.

b

• = . * * * . * . * = * * .* .. * * * * * * * * * ' * * *

......g.g.

j

.. .., .,..,. ... .+ ..... .. ...

. .*+ ........g

. .g . . . . . . .*** . . . . . .... ....

g...** l g..........o...

. . . . . g.. . . . . .

. . . . . . .... . . . l.

. , , . .. ...* . . *. .* .* .= .* .* .* .... . ,

. . ...~

....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... .. ... ...... .. ... . . . . . . . . . . . . .I

. .... l

........ j

. . .. .. . .. .* .. ... . . e......................................................................

... .. .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ... .. . .. ... . . . . . . . . . . . .. t

,...... .......... i

. . . . . . . . . . . . . . . . . . _ . . . . - . . . . . . . . . . . . . . . .. .. ... .. .. ... .. .. .= . . . . . . . . . . . . . . . . -. . . .

d?8 ' ji t grg N!xtnas sued oJ sluf ol nu!1 atiit pjsal op8 !u

Fil.$.83

. 4 . m . .. . . . . . . . e. n ic m.

t. TAP

..."."l "2 :..!! : '"2;.:0;;

. li. .:.:::t.

I *i!'  !.!!M. ,

!. 3. :....

. . - ,. ...,i. .u...,,.i.... .............

Fig. I 11.5.34. Associated data for unit rnap of single unit with offset origin EXAMI'LE 3 A 2x2x2 UNREFLECTED ARRAY OF CONCENTRIC CYLINDERS IN CUllOIDS The physical representation of this example is a 2x2x2 array of the configuration described in Exumple 1 of this section. The input data description for this array is given below:

hh2 RARE ARRA >' 0F CONCENTRIC C)'LINDERS IN CUR 0lu READ PARA AI RUN-NO LIR-41 TAIE.8.5 END PARAAI READ h!!XT SCT-l AllX-192300 4.7048 2 AllX-2 2001.0 Al!X-3 302 0.1 bilX-4 2001.0 END hilXT READ GEDAf C)*LINDER I I 2.6 2P13.0 C)'LINDER 013.6 2Pl5.0 C1'LINDER 413.8 2P13.0 CURotu O I 4P3.8 2P15.0 CURoth 214P4.3 2P16.0 END GEGAf READ ARRAl'NUX-2 NU)'.2 NUZ=2 END ARRAl' RL40 PLOT TTL 'X l' SLICE A T llALF llEIGilT OF ROTT0h! L4l'ER.*

XUL- 0.3 lyL-17.5 ZUL-16.0 XLR= 17.5 l'LR 0.3 ZLR-16.0 UAXu 1.0 VDN=.I.0 N4X-130 NCll.' * .X* END l TTL 'X Z SLICE TilROUGil FRONT ROW, l'-12.9.'

XUL 1.0 )*VL-12.9 ZUL.65.0 XLR= 18.21'LR=12.9 ZLR= LO UAX-1.0 WDN- l.0 NAX-60 END END PLOT END DATA END As stated at the beginning of Sect. Fil.5.10. the origin of the plot is located at the lower left back l corner of the array. Each individual unit in the array is 8.6 cm wide in x and y and is 32 cm high in

'. z, Since the array has two units stacked in each direction, the array is 17.2 cm wide in x and y and is -

l 64 cm high. Therefore, the array exists from x=0.0 to x= l7.2, from y=0.0 to y=17.2 and from

. z - 0.0 to r - 64.0.

_ . - . ._ . . - - . _ _ . ~.

Fi l.5.84 The first printer plot is to generate an x.y slice through the array at the half height of the first layer.

as shown in Fig. Fil.5.35. This occurs at z-16.0 cm. It is desirable to define the outer boundaries of the array. This is achieved by setting the boundaries of the plot larger than the array. In this case, the boundaries were arbitrarily set 0.3 cm larger than the array, resulting in a border of question marks -

around the array. If the plot were to exclude everything external to the array, the following coordinates could have been entered XUL-0.0 YUL-17.2 ZUL-16.0 XLR-17.2 YLR-0.0 ZLR-16.0. This would have climinated all the question marks. The existing picture was made. using XUL-.0.3 YUL- 17.5 ZUL-16.0 XLR - 17.5 YLR-.0.3 ZLR= 16.0.

,,,,,,,,,,,,,,,,,,,,,,,,,...,.,..,.,..,.,.,..,.,.,,,,,,,,,,,,....,...,...,..,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,m,,.,i.,..,.,",,,,,,,,,,,,,,,,,,,,,,

. ~ . . . . . . . . . . . . . . . . . -_,,

Fig. Fi1.5.35. x.y plot of 2x2x2 bare array The second printer plot is to generate an x.z slice through the cenw of the front row of the array, in-order to obtain a boundary of question marks, the coordinates of x and 2 were arbitrarily set 1.0 cm larger than the boundaries of the array. The center of the front row occurs et y=12.9. The coordinates of the plot were: XUL--l.0 ZUL-65.0 YUL-12.9 XLR-18.2 ZLR--l.0 YLR-12.9. The plot was defined to be half a page wide by entering NAX=60. The resultant mixture map is shown in Fig. Fi1.5.35.

, , -.1 -, , ,_,- , . . ,- _~ - - - - . . - , - , - , , , ~.-. ,

-s ~-

1 1:1l'i$raiS .

.4,,

4, .44 . 4,d.... .dd . 44 .8. d.8...

.,,,...4.44..,.,...4....44444........d....A..4..4.4......e.....,,.

....a. .. .. .. .. .. ... . . .. . . . . .... ...

. . .o

... .. . . . . . . . . ...a.

..a..

..a..-

. . . . . . . . . .. . . - 4

...a..~.....

,a,,,,- . . .... . . . . . . . . . . . . ...

. ............... ~...

.. .. .. .~.. .. .. ..... ..... .. ... .. ..... ..... .. . . . . . ....... ....... ... .... ... ....... ....... ... ...

.. .. ..- ~.- . . . . . . . . . . . . . . . .. ...............- .... . .

. ............... ....4

...... . . ~ ... . .. . ... ... . .. . ... .. . . . . ................

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

. ...- ..,... ~ . . . . . . . . . . . . . . . ...

.. .. .. .. --. . . ................ ............ 4.. ................ ...

. . ~ .. ....... ................ ... ..

. ... . ... .. ... .. ... .. ... .. ..... ..... . .-. .a..,. . . . .

,a.... .............. ..

, ... .. ... ... . . . ....... .. ... .. ... .... . . .... ...s...........

. . . . . . . . . . . . . . . . . . . ..... . . . ..a..

a...

, . . , . ................ -. . .. . .. ... ... ... .. . .. . . . . . . ..... ........ ....... .. .... ...... .. .. ...a... . a -

. , .. ... .. . . . .-?.- ...a s..

.. ... .. ... .. ... .. . .. .. . . ... .. . .. .. .. . .. . . . . . . . . . .....a.

a

. a .a.

, . ~ . ................

~ ............... ..- ...................

.a~ ............... ...- -

a,.... .. ............... . .- . . . .... . . .. . .. ... .. . .. ... .. . . .. .. .... . . . .

. ... ~ . . . . . . . . . . . . . . . ... . . . . .. . .. ... ... ... .. .. .. .. ,.,. . . . .

...~ . . . . . . . . . . . . . . . ...

..a. a d.d...........ded......ti..d,..444....d.,.,.........,..............

4 464.. 44 .d......d.ed.a.

I% 31irc9. x.z d[ot p txgxg qcu eh

. --~ - ~ . .- . . . . ,- . . - - . .. --

+

Fi 1.5.86' ~

EXAMPLE 4. A 2x2x2 REFLECTED ARRAY WITil T11E ORIGIN AT Tile LOWER LE -

IIAND HACK CORNER OF Tile ARRAY The array'is the array described in Exampic 3 of this section with a 6-in. concrete reflector on all faces. The input data description for this array is given below.

2x212 REFLECTED ARRA Y OF CONCENTRIC CYLINDERS IN CUBOID READ PARAM RUN=NO LIB-41 TME=0.5 END PAMM READ MIXT SCT-1 MIX-192500 4.7048 2 MlX 2 2001.0 MIX-3 3011.0 MIX 4 2001.0 END MIXT READ GEOM CYLINDER I I 2.6 2PIS.O CYLINDER 013.6 2P15.0 CYLINDER 413.8 2P15.0 CUBOID 014P3.8 2Pl$.0 CUBOID 214P4.3 2P16.0 CORE I i 3*0.0 REFLECTOR 3 2 6*$.0 J REFLECTOR 3 5 6*0 24 I END GEOM READ RIAS 1D-3012 5 END BIAS READ ARRAYNUX.2 NUY-2 NUZ-2 END ARRAY RE4D PLOT TTL='X Y SLICE AT HALF HEIGHT OF BOTTOM LA YER. INCLUDES REFL.*-

XUL=-16.24 YUL-33.44 ZUL 16.0 XLR=33.44 YLR= 16.24 ZLR 16.0 UAX=1.0 VDN=-l.0 NAX= 130 NCH=' * .X' END TTL='X-Y SLICE AT HALF HEIGHT OF BOTTOM LA YER, INCLUDE 3 CM OF REFL' XUL.-3.0 YUL=20.2 ZUL.16.0 XLR= 23.2 YLR= 3.0 ZLR=16.0 UAX 1.0 VDN= 1.0 NAX-130 NCH= * * .X' END ,

l-TTL= 'X-Z SLICE THROUGH FRONT ROW, Y-12.9. INCLUDE REFLECTOR'_

XUL=-16.24 YUL.12.9 ZUL-80.24 XLR=33.44 YLR=12.9 ZLR=-16.24 UAX= 1.0 WDN=-1.0 NAX= 130 END -

TTL 'X-Z SLICE THROUGH FRONT ROW,- Y-12.9. INCLUDE 3 CM OF REFLECTOR' XUL=-3.0 YUL-12.9 ZUL-67.0 XLR=20.2 YLR=12.9 ZLR= 3.0 l UAX-l.0 WDN=-1.0 NAX=130 END

l. END PLOT l END DATA END 1

The CORE _ card specifies the coordinates of the lower left back corner of the array- to be (0.0,0.0.0.0). Thus the reflected array extends from 15.24 cm. toy 32.44 cm in x and y and from --

, -15.24 to + 79.24 in z.

l, The first printer plot fer this example is to show an x y slice through the array and reflector at the half height of the bottom layer. A border of question marks is used to verify that the entire reflector

"=

has been shown. This is accomplished by arbitrarily setting the picture boundaries I cm beyond the -

reflector boundaries. The coordinates used for this plot are: XUL= 16.24 YUL-33.44 ~ ZUL-16.0 XLR =33.44 YLR= 16.24 ZLR-16.0. The plot data description is shown in Fig. Fil.$.37, and the plot is shown m "g. Fil.5.38.

. . ._s. - -- m . . .m _ - - . - . m ,

4eJ28 paiootjs2 gxtxt jo scid X-x grg*It3 S!3 4 4 84. d.4 4 4. A. 44, d.4 8 8 44 44 44 4 4444 44 4 44 444 4 4 8 4. #.d. 4. d. 444 448 8 .4- 4 4 4 4 4444 44 444. &. d. 444. d.8 8 4 44444.d. 4,4 44 44 8 44 44 44 4 444. d. 4 4 4 4. 4. d. 8 4 4,8 44 8 4 04 4 4. d.8 4. d. 44 4 4 4 4 4 4 4 die gg - - -

.ggg gg.. . , + - + , . ggg -

4g.. < r 6

• r n c ggg gg.s s a e * < 1

. ggg gg.. + 4 + ~

gg.. , + + * *

'..ggg 44 " * * * * "'444 44..* + , , * * + 4 + + ..' eggg dd 44**** ** ** * * * * * * *

'*4d4 e 4 ,A. * ,

• gg e.

gg.6 , , , * + + '*'.ggg 444

- 44 gg,.*' e , e , <*

• 36 ' .' ggg 4 d44 g4 4 * + ,*

• 4 e , , , *- .aggg gg.a .. . m , , 4 + .

.gg.. . e , + ** * , +

i.agg

+ . gg, 44' ' ' ' + * . '* *

' e*A de'* * * * ' ' * * * * * * * * * * * ' * '1 gg.s *

• 6 e = + , , i * * ,',,

ed * ' ' ' ' ' '

d44 ggo , + A + + e +64 4 6+ + + ..ggg gg. 34 . + + e k 4.e44 gg.. o , , a * * - . + . * + ..ggg

.gg.. . + + 4 ,, , + n e e e 4 h 4

id e

dde 4 4 ' ,'

gg. 4 '*

• g g *** 3 3 , * +

• dga

.gg=. *

• 3 g * *

• g g * * *

• • dde ga+' + * * ** *

' *

• 3 tooeeeee 3 *** 3 eseessee 3 * *

• 4aa de** + ^

• • • • 8 otoeososeet *** eteese e* **e 5* **444

'+ ** * +

4d

• eeeeeeeeeesso 3***3 eseeeeeceesee *

'444

• * * *3 - eeeeeeeeeeeeee - * *

• 3**

44 '

b ' * **

eeeesseeee poes +

' dde

. 446' **t osoemeeeeeees * *

• eseeeeeeeeeee B+' * *

'444 44 * * ** *eeeeeesosee f ** a t ee********ee m '

ide 44** ' * ' * * * * ** *e se ********** I*

ag** * * + * +4'*+ *I eeees I *** 8 3 + + + eees, * *

' ' f ed

' age de

' '

• I I *** 3 I f *"* ~*dde 4d'* * *** FTTT1 * * '

ded ag.. 4 + > + +a + ...** . FT.TTI* * * * * * *

'

• d ie g . *** *

• FTtt1 EItrl add 4

ag.4 ' '. *

• g - - . g 3 * * '. *' sag

&&

• 4 9 +

• eoese k * *

• 5 eeooo *

• 44 + + + * *B eesseseeee t *** B se sees s e e s I* ^444

.id ' *

• emesseseeems g * ** 3 eseeoooooose * * *'ed ad ** * "*t eeeeeeeeeeese * * *

• e see s***es ee f*** ** **'ded sed 44** * * * *

• • f o***o****eeste * *

• se*ees* *eooooo 5 '

de*'+ ' ' " "* ooeoomessesse t ** 3 eeeeesseeseee *' ' 'ded

' te d de '

• 3- oossesseees * = = eeeeeeeeeee t*

• de' '

• 3 ********' S *** I e ***eese E '* 444 44**' ' ' ' * * * * $ R *** E $ * id a 44 '

• 5- S ** I I * * 444 de ***************************************** d el gg,. 6 + + r a , 4 i' ed ggge de

gg.. + 6 6 ' .'ded ggg ggo. e 4 + + a

..ggg gg. , a + + 4 +

ggg gg.i , . +,, m

..g,g

. 4 4 '

"'ide 44 ' .' r.'444 e, gg. e a e + 4 6 *

. gg, gg..

gg , =

e

-. gg g 4

'.g,g

$4"' ' ' ' '

44 ' ' '"idd 4a . . -'d84 da 44.. d..

d,.. , ,

At**

44 ' ded

- de id4/d a de

4, de'*

di .d d4 . - ide J se'* " ad,

' 44444 d d 4,44... 4 44 4 4 4 4444 4484.. 4 44 444.8.. 4. 4 d48 844 44 4,,,4. 4 4 4 4.44444 44,44.d 4,4&4.dde d4444,4 e d d...... d 4d 4e 4 4 4 4 4 4 4 4 4 44 4 4 4 44 4 4 4 44.dd44 8

.... d d .d.d 4844. ..d 4 4 4 4 4 4.d 4d d.,4 . .44 4 4 4. e 4 4 4 5 d d 4 4 4 4 4 4 4 4 d d 44 4 to o[dmsva jo says X*x Joj niep 1old 't.CS'ild '8U i........ *.5.. ........*.,.. .. 4. .. .

.d d .., .,,a.d ..,.

......... ....e,..

....e.....a

...... .....c.* .

. 4 .. 3 . . . . . .

4..., .d., .....

, . * . .i ....

- . e e. . . . . . .

',d.. . ,=i m . ,. 4 .. ,,,. .. n ,. ...

e 0

LSTild t

e D

\.

Fil.5.88 Tbc next printer plot is the same as the previous plot except the plot includes only the first 3 cm of the reflector. This results in the picture being large enough to show more detail. The coordinates used for this plot are: XUL-e3.0 YUL-20.2 ZUL-16.0 XLR-20.2 YLR-e3.0 ZLR-16 0. This plot data description is given in Fig. Fil.5.39 and the plot is shown in Fig. Fil.$.40. e

. . . m . n m . ..i m o m m m .. i.a o. > c. o m e mm. m

...m. . , , .

. . .so s * .

.,e, . o.e . o.,

000. D E A 83 000 01 87 8

. ,i.e...., .,......,

. a. .e.. .. .. a, ..

..o....,

O..e.A.A.l l

. m 4 4415..

., ,. .e ne . . u, ,...e... ... . . . . . . . . .

Fig. F11.5.39. Plot data for enlarged x.y slice of example 4 E titas AE . 33311432 ..

E2 E R312 .. &&AE ESA ..

BE E3 . 33 12 ..

• EA En e... EJ SE ...

A seese e .. t eseeee a ..

. as eeeeeeeeeeeeese 4 . . 33 eeooseeeeeeeeee 33 ..

. 3 eeeeeeeeeeeeeeese*e EE . 85 esseeeeeeeeeeeeee*e 8 .

s ** eseeeeeeeeeeeeeeeeees 33 EA e e e e * *ee e ee e ** e c e e *

• ee s E

. 3 eeeeeeeeeeeeeeeeeeeeeeees aa .. .... . E

. . . . . S **eeeeeeeeeeee eeeeeeeee*e eeeeeeeeees e****e eeeeeeee ee a ..

3..

.a sees ee eeee****ee**eoecese**

.3 eeeeeeeeeeeeeeeeeeeeeeeeeees s . . .. 3 eeeeeeeeeeeeeeeeeeeeeeeeeeee E ..

,.s seeeeeeeeee eesse eoe ocee e eee et 3.3. ... 13 eseeeeeeeeeeeeeeesseesseseese 3...

...a e s se ee ee e ee ee eeeeee e e e eeee ees 3. . . a * * * * *

• e e e e e * * ** *

• u e s e * *

• o * * *

• 3..

.3 es s eseo**eeeeeeeeeeeeeeeeeeee 3. .. 3 eeeeeeeeeeeeeeeeeeeeeeeeeeees 3..

• • • • • e*******o*********ese*** 15 . . . 52 ee****esesoseee**o********o** 8..

.B 3 ooseeessseseeeeeeeeeeessseee a . . .. a se e ee e e e e ee ee eee e e e e e e* * ** o

• I...

...g s e ee e ss ee e eeeeeee e ee eee e e ee 3.. 3 eseeeeeeeeeeeeeeeeeeeeeeees 3 ..

. 32 eeeeeeeeeeeeeeeeeeeeeeeee 3 ..... 3 e e e ee e ee eee ee e e e e ee eeeees 32 . _

a oesseeeeeeeeeeeeeeeeeee 58 .... As se e*o* *e s se** **e* * * ** e* E ..

. . 3 e e ee ee e e ee eee ee e ee* BJ ..... as s ee seeee e eee e e *** e e 8 . . .

.. Es eeeeeeeeeeeeeee as . . . . . as eteeseeeeeeeees as ..

.. Es cose*** 3 . . . . 5 e * * *ee s EA ...

SA SS .. .. SS LA e .

. 1E RA . * * . 55 55 ...

Als RAE , .. 114 EAR ..

gan a n agag ... . . .

.. . . . . .. .. . . . .. . .. . . ... . 333A13....... 4 E2 . . . . . . . . . . . . . . . . .

, . . . aaeeseaeu ... 321821115 ..

- EAR SES .. . KS8 Ett ..

. 12 M . . . EA 11 *.

. 12 42 ... U && ..

.. ta eeeeeee 3 . . . 3 eseeees II ..

.. En **eeeeeeeeeeees sa .... 12 eteeee****eesee La ..

eees* *ese**ee eeeses 3J 3a eeeeeeeeeeeeeeesese 3 ..

. a E

e s e e ee eee e ee eee ee e e ee e s eesseeesesseeeeeeeeeeeese 33 . . ... IA 5 e t e* * * ***ee s ee e e ee ee e **

• *

• e *e cese s e ee ee eeee *** e e 3 ..

EA ,,

. 33

. 3 e t e e e e e e e ee eeeee ee e e ee e e ee s 33.....

.....E ooesesseeeeeeeeeeeeeeeoesee 3..

.. E se e se s ee ee ee e e eee e ee eeeee e e e I m.... 3 eseeeeeeeeseeeeeeeeeeeeeeese 3...

,.E eeeeeeeeeeeeeeesseeeeeeee eees 13.....R3 e** *

• ee seee eee e e eee s **ee * * * *

• 3..

..g eeeeeeeeeeeeeeeeeeeeeeeeeeeos 3,. ,.3 eeeeeeeeeeeeeesesseseeeeeeeee 3...

...g seeeeeeeeeeeeeeeeeeeeeeeeeeet 3.....E eeeeeeeeeeeeeeeeeeeeeeeeeeees 3..

..3 e s se e s e ce s es ee s s e see eee eee ee s 13 .. 12 e eee e e eeeee e eee e e e eee ee* ** e e. 4..

. I seeeeeeeeeeeeeeeeeeeeeeeeee* I ** ****secosee** e**ese**eesee 3 ..

.. 3 esseeeeeeeeeeeeeeeeeeeeeese E . . ...E .E oe**eose e**esesseseee ***ese 5*.

E *e ee es e o ** ee ee e e e e* *** *e e t . +.. R * *e s e* o **ee** ** *e *o** e*e e R .+

3 eseeeeeeeeeeeeeeeeeeeee as .. La e e ee ee ee ee ee e.e eee ee ec e 5 ..

. 5 ee**ec ee ee e*o**eeee 45 .. . EA *****eeeeee eeeeeeev E ..

12 e sse *** * *e es e e o 13 . . . . SA e se*** *ese* ** e

• EE ..

. E e***** a .-.. E s e*e se a .

.. El 11 . . 13 LA -.

.. L2 K3 . . . - EJ Et

. 422 1453 ...~ 1113 313 ...

4.. R E A122.42 * . Et 8aerea ...

Fig. Fil.5.40. Enlarged x-y plot of 2x2x2 reflected array

FI1.5.89 -

The third printer plot for this example is an x z slice through the center of the front row. ' An extrr.

I cm is included in the coordinates to provide a border of question marks around the plot. The coor-dinates are: XUL.16.24 YUL-12.9 ZUL.80.24 XLR-33.44 YLR-12.9 ZLR--16.24i The result-ant plot data and plot are shown in Figs Fil.5.41 and Fil.5.42.

. . . .u r m ... .. . .. u . . . i.cs.= .. 6.cm

., m.. m "I'!!:' '

! ' ': E

::: .. I"::i!!::

....... ...,i ::::!

l !u.....

i."'t ?J:: ..

u. m.,....u.... m......,u...

Fig. Fil.5.41. Plot data for x z slice of exampic 4 w

h

.,e-

-- w ------ . y

Fi l.5.90 4 .

Fig. Fil.5.42. x.z plot for 2x2x2 reflected array

F11.5.91 The last printer plot for this example is the same as the r vious one except only 3 cm of the reflector is included in the plot. The plot data and associated plet are shown in Figs. Fil.5.43 and Fl 1.5.44.

...................in....c...,s.m.

.a m. . .A.

. . . . . . . . , > i .

t 00$t 1841.. Coomstua.$.,

. . . ... .. .. . .. .. . . .i......,

. AA I S T Aa l =

t .05e , t AC Du. . *

. > > . .. i i. ..s. ......... ..s.........,

Fig. Fl1.5.43. Plot data for enlarged x z slice of example 4 9

- - - - - - .~ - - - . - . - , ,

e

' 1)

- I'l l e 5.9'2 e

e 9 4 ft t d C+ft34 eq$9 td f f flg 4 t t S $1 g 4 e 4 4 b + f i 4 . x e e n te *m.

1 79 9 S t 'i t t if 9 i - 3 4 4 Jsy f f & + n 4 g I

t + 4 4

5 . th e e .

I f y

.2... . . . . . + .. ....

. . . . . . . . . . . . .. . . . . . . . , , .,. .e....... ...... . ,.

...r- . .....a . . . . . .... . . . . ..o*...4.=e.s.o.ee..e... . . . . . . .... . . . . . . . . , ,

, . . . . . ......g...,......... . ... .. . . . . . . . . . . . . . . . . . . . . . ........o.........e#...,.... ,,, , j

.3 e e ee e ee ee e e e e eee ee ss ee e e e e ee s 3. . .. 3 e e eeeeee e ee e e e e e s te ese eee ee e e 3... , ,

..3 eeepseeeeeeeeeeeeeeeeeeeeeese 3,...3 eeeeeeeeeeeeeeeeeeeeeeeeeeeee 3... ,

.. 3 ee eee e e e ee e e e e e e e e ee e eee e ee e e 3.. . 3 eseeeeeeeeoteeeeeeeeeeeeeeees 3...

3 esseeeeeeeeeeeeeeeeeeeeeeeees 3.a ******* e se e*e**eo o oe e e e e e e es e 3..

4. 3 oeesseeeeeeeeeeeeeeeeeeeeeeee eteeeeeeeeeeeeeeeeeeeeeeeeees 3....3o. 3 eeeeeeeeeeeeeeeeeeeeeeeeeeees 3...

..3 3...., se e ee e e e ee ee e ssesee e e e e ee e e e s

.3

,.-3 eeeeeeeeesseeeeeeeeeeeeeeeees eeesteseeeeeeeeeeeeeesseeeees 3...3-33 3 , e..

ee e e e e e eeeeee eee ee ee e ee eeee s e eseeeeeessees see ee*ese**o*ees 3.e go. ,

3.

. ese***eseee ee eeeee eee ee eeeeee 3 . . .- . 3 eeeeee***eeeeeeeeeeeeeeeeeees ,

..-33

. 33.....

e e e e e e e e e e e ee e e e ee eee e e e ee e se 3,. .3

. s e sseeeeeeeeeee t ote s*** et ee *e 3 . . .* . 3 e eeeeeeessesseosseeeeee,eeeees

• eseeeeeeeeeeeeeeeeeees eeeee g...

.-33 eeeeeeeeeeeeeeeeeeeeeeeeeeees 3.e .. . eeeeeeeeeeeeeeeeeeeeeeeeeeee, 3.., ,

.3 segeeeeeeeeeeevose**esesseees 3. . 33 eeeeeeeeeeeeeeeeeeeseoseesese 3 .. , ,

,og see eeeeeeee eesee*****o**eeese 3.e .3 steeeeeeeeeeeeeeeeeeeeeeeeese 3... ,

..y eeeeeeeeeeeeeeeeeeeeeeeeeeees 3....3 e e s e e ss eee e eee ee e e e ee e eee eees 3.+. , ,

.3 eeeeeeeeeeeeeeeeeeeeeeeeeeeee 3., .3 eeeeeeeeeeeeeeeeeeeeeeeeeeees 3..,

3 esseeeeeeesseeeeeeeeeeesse**e 3.. w.3 se e eeee ee e e eer se e e e e e ee e e e ** e '

3-..

..a s e e e e e e e e ee e e e e eee e e ee e e e e e e s 3 . . .. 3 Seessesseeeeeeeeeeeeeeeeeeeet . . so.

.3 eeeeeeeeeeeeeeeeeeeeeeeeeeece 3 .. . . 3 . e e e e e e e ee e ee e e eee e ee e eee e e ee s 3...

,,_3 e s e e e ee e e ee ee ee e e e eee e e e e e e t s 3., e3 e st a t os ee e ee e ee e e e e e e e e e e e e c e 3.,

.3 eeee eeeeeeeeeeeeeeee eeeee e ee s 3. . 3 *

• e c e sse e e e e e e e e e e e e e e e e e e e e e 3..e

.3 e e e e e ee ee e e e ee e e e ee e ee e ee e e c e 3 .. . 3 **eseeeeeeeee e eee e eeee se**e6e See y

.3 eseeeetooemeeeeeeeeeeeeeeeese 3.. . o . 3

• e e s e s s e e e ee ee ee ee ee eeee e ee e s 3., ,,

..3 eeeeeeeeeeeeeeeeeeeeeeeeeeees 3 . .. e . 3 ee e e ee ee ee e e e e e e e e eeee e ee e e os su

..e se e eee e e e ee e e ee e e ee e e ee e e ee v e 3.e

• 3 e*eeeeee*eseeeeee***e******** 3.*.

,.3 es e e e e e eeesse se eee e eee e e e e e s e 3 . .. . 3 eeeeeeeeeeeeeeeeeeeeeeeeeeeeg 3. ,

, seeeeesseeeeeeeeeeeeeeeeeeees 3.. .3 e e e e e e e eee e ee e e e eee e e ee e e e e e e 3 ..

.~33 esteeeeeeeeeeeeeeeesesseeeeet 3. . . . 3

..3 esseeeeeeeeeeeeeeeeeeeeeeeees 3 . .. . 3 e o ec e seee ee eeeeeeee eeeeeese***eseee eee eeeee ee40s eee e e e33.,., e.e,s , ,

1

.3 eeeeeeeeeeeeeeeeeeeeeeeeeeeet 3.. . . 3 seeeeeeeeeeeeeeeeeees seeseese 3...

.3 eesseeeeeeeeeeeeeeeeeeeeeesce - 3 .. .. 3 e a s ee ee e ee eeeeee e ee e e ee e ee ee s 3.** ,5 . .

._3 ee e ee e eeeeee e e eee eeee e ee ee e s e 3....+3 e e e e ee e eeee e ee ee eee ee ee e e e eee 3..

.3 e e e e e ss ee e e e ee ee ee e ee e e e e ee e t 3. .. . 3 eeeeeeeeeeeeeeeesseeeoosessee 3..... + , , ,

.is eesee*eteeeeeeeeeeeeeeeeeeese 3 . ... 3 s e e e e sos e e e ee e e e ee e eee e ee e e e, 3. , ,

.3 esseeeeeeeeeeeeeeeeeeeeeeeees 3. ... 3 e e e ee eee ee e eee ee e e ee e e e e e ee es _ 3.,., , ,

.*,.3 ee****seeeeeeeeeee e ee eeeeee e s 3....3 eee ee eee e eeeee ees see e e e g g e s se 3.e.

.. 3 e e vouse ee e ee e e e e es s e e e e e e e e es 3.. 3 seeeeeeesseeesseeeeeeeeeeeees 3...

mq es tese e e e eeee e eee e eee e e e eee e s 3....3 *

• e *e o**e **** ee e e e e e ***e e * *e e 3 ..e ,

.3 eeeeeeeeeeeeeeeeeeeeeeeeeeees 3.. 3 eseeeeeeeeeeeeeeeeeeeeee**eet . . 3.... ,, , ,

.3 eeeee**eeeeeeeeeeeeeeeeeeeees g o . .. 3 eeeeeeeeeeeeeeeeeeeeeeeeeeeee 3.,. ,

.. 3 e teeee e e ee e eee e ee eeee e e e e e e e

• 3..e==3 m e***o***eest e s e** **ee seee e e e 3., , 4 33 e e eee ee ee e eeeee e ee e e e ee ee e e s e 3.. .3 e s ee e e eee e eeee e e eeee e ee ee ssee 3... , ,

4 ,3 ee e eee ee ee e e ee e e ee e e e e ee e e ee s 3..... eseeeetsseeeeeooesseeeeeeeese 3...

.3 s e e eee e e ee ee ee ee ee e e e e** e o o s e 3 ... . 33 eeeeeeeeeeeeeeeeeeeeeeeeeeece 34

.3 e e eee ee e eeeee e eeee e e e e e e e e ee s 3....3 eeeeeeeeeeeeeeeeeeeeeooseeese 3.. ,

.3 eeeeeeeeeeeeeeeeeeeeeeeeeeeee 3 < ... 3 eeeeeeeeeeeeeeeeeeeeeeeeeeeee 3...

e s s eee e e o og e ee e eee e ee e e e e e e se eeeeeeeeeeeeeeeeeeeeeeeeeeeee

,*+3

..3 e e e e eeeee e e ee e eeee ss e ee* **

• e 4

' 33 .....,3.3 etee**eeeeeeeeeeeeeeeeeeeeeee 3... i ,

3 e, ,

.3 seseeeeeeeeeeeeeessseeessesee 3.s..3 e tee eeeeee ee es sesseeee ee eee c e 3 e.

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Fig. Fil.5.44. Enlarged x-z plot of 2x2x2 reflected array I

t

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Fig. Fil.5.44 (cont.)

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y ye+ m,e

I Fi l.5.94 EXAMPLE 5. A 2x2x2 REFLECTED ARRAY WITil Tile ORIGIN CENTERED IN T11E ARRAY Th;s example is physically identical to Example 4. The difference is in the specification of the ori.

gin. The bare array is 17.2 cm wide in x and y and 64 cm high. The origin (0,0.0) can be placed at the exact center of the array by specifying the lower left back corner of the array as x=-8.6, y=-8.6 and z = - 3 2.0. This is done using the CORE description. Because the origin is located at a different posi-tion, the coordinates of the plots will also be different. The input data description for this example is given below. -

2x2x2 REFLECTED ARRAl' OF CONCENTRIC C)'LINDERS IN CUBOID READ PARAhl RUN.cNO LIB-41 TAfE=0.5 END PARAAf READ AllXT SCT= 1 AllX-192300 4.7048-2 AllX= 2 2001.0 AllX=3 3011.0 AllX-4 2001.0 END AllXT READ GEOAf C)'LINDER 1 ! 2.6 2PIS.0 C)'LINDER 013.6 2PIS.O C)'LINDER 413.8 2PIS.O CUBotD 014P3.8 2PIS.O CUBOID 214P4.3 2P16.0 COREIi 2* 8.6 -32.0 REFLECTOR 3 2 6*S.O 3 REFLECTOR 3 5 6*0.241 END GE0Af RibtD BIAS 10 3012 S END BIAS REA D ARRAl' NUX=2 NUl'=2 NUZ= 2 END ARRAl' READ PLOT TTL='X-l' SLICE AT llALF IEEIGitT OF BOTTOAf LAYER. INCLUDES REFL.*

XUL -24.84 l'UL= 24.84 ZUL=-8.0 XLR= 24.84 l'LR=-24.84 ZLR=-8.0 UAX=1.0 VDN=-1.0 NAX= 130 NCil=' * =.X' END TTL='X l' SLICE AT HALF llEIGHT OF BOTTOAf LAl'ER, INCLUDE 3 CAI 0F REFL '

XUL=-11.61'UL= 11.6 ZUL -8.0 XLR= 11.6 l'LR= il.6 ZLR= 8.0 UAX= 1.0 VDN=-1.0 NAX-130 NCH=' * .X* END TTL *X-Z SLICE THROUGH FRONT ROW. l' 4.3 INCLUDE REFLECTOR' XUL.-24.84 l'UL-4.3 ZUL-48.24 XLR=24.84 )*LR= 4.3 ZLR=-48.24 UAX-l.0 WDN=-1.0 NAX-130 END TTL 'X-Z SLICE TilROUGil FRONT ROW, l'=4.3 INCLUDE 3 CAf 0F REFLECTOR

• XUL.-lI.6 l'UL-4.3 ZUL= 33.0 XLR-1L6 l'LR=4.3 ZLR= 35.0 UAX= 1.0 WDN=-1.0 NAX=130 END END PLOT END DATA END The first printer plot for this example covers identically the same area as the first printer plot for Example 4. The plot data for this plot and the actual plot are given in Figs. Fil.5.45 and F11.5.46.

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Fil.$.96 The Exarnple 5 plot data and associated plots for an enlarged x.y plot, an x.z plot and an enlarged x.z plot are given in' Figs. Fil.5.47 through Fil.5.52.

..u...,m u,.=u. mu.im >uu.m.

.imu m

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Fig. Fil.5.47. Plot data for an enlarged x.y slice of example 5

._ . .. ._. ~_ . . _ . . . . . ...

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un .....

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Fig. F11.5.48. Enlarged x.y plot of 2x2x2 reflected array with centered origin

,1 _, _ _ _ _ . _. . _;,.. _ . _ _ . - . - _ .. ., _ .... ._.

s T

F11.5.97i .

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Fig. Fi1.5A9. I' lot data for x r slice of example 5 f

i:

r:

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- F11.5.98 ' y

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Fig. Fil.5.50. - x.z plot of reflected 2x2x2 array with centered origin

.6

nm - , . _ .. _ / _c , . - . ,, , , , ,

I 4

i F11.5.99 -

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... .u,.,,. i i. ..$.. . . . . . . . , ..i.. .........i Fig. Fil.5.51. Plot data for enlarged x_-z slice of example 5

-j

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1 i

r -j l

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s ---r

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T 4

e .

Fi l.5e100' Y a

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3.,

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Fig. Fil.5.52. Enlarged x-2 plot of reflected 2x2x2 array with centered origin

. . - - -- - - - .- -. . ~

f711.5.l()1 t

l l- .. .......................... . ...................... . . .

t .... . . . . ............................

4 I

1 Fig. Fi1.5.52 (cont.)

t-l

. - _, . - - . . - - . . - - - ~ - . - , _ - _ . . ~ . . . - _ - - - . - ~

-l

- F l 1.5.102 4

EXAMi'LE 6. NESTED llOLES Refer to the nested hole. description of Sect. Fil $.6.2. The mixture map for this problem is shown in two parts in Figs. Fil.5.ll and Fil.5.12. This example is one that involves a reasonably complicated placement of units or box types. Therefore, it might be useful to the user to generate both a mixture map and a unit map for the problem. Liecause an enlarged printer plot of the mixture map -

was already presented in Figs. Fil.5.Il and Fil.5.12, the mixture map in this section was reduced to -

fit on one page width by changing NAX from 260 to 130. The resultant mixture map is shows. in Fig. Fil.$.53 and the unit map is shown in Fig. Fil.5.54. The data description for Example 6_ .

follows, i

a 4

. . - . - - - - ., ...ww,--..c., -.Ar,.-,--r-.w,.,w.- ,, w. m . .-,--,--,-~%..,,-,,v-.. - - , - - ,-- ---vr--,-,.~. - ,E.,.-. ...-,..,r-.. ,----e,,, c._ - - -

Fil.5.103 '

=KEh0!-

^ NESTED fl0LES SAMPLE READ PARAAf RUN NO LIB 41 TAfE 0.3 END PARA Al READ MIXT SCT=1 MIX =I 92500 4.7048 2 MIX.2 2001.0 AllX.3 502 0.1 AllX.4 2001.0 -

END MIXT RE4D GEOM UNIT I C1'LINDER I I 0.1 27110 UNIT 2

' CUBoth 212P0.12PO.05 2 PILO UNIT 3 CUButD 212PO.05 2P0.12Pl$.0 UNIT 4 CYLINDER I I 0.12 PILO CYLINDER 3 I 0.5 2 PILO IIOLE I 0.0 V4 00 ll0LE I 0.4 V0 0.0 llOLE I 0.0 0.40.0 ll0LE I .0.4 0.0 0.0 ll0LE2 0,2ILO00 Il0LE 2 A2 0.0 0.0 il0LE 3 A0 A2 0.0 IIOLE 1 0.0 0.2 0.0 UNIT 5 CYLINDER I i 0.5 2 PILO UNIT 6 CYLINDER 210.2 2 PILO UNIT 7 CYLINDER 210.2 2 PILO CYLINDER 011.3 2 PILO Il0LE $ 0.7071068 2*0.0 ll0LE 6 A7071068 0.7071068 A0 il0LE 4 A0 0.7071068 0.0 ll0LE 6 0.7071063 0.7071068 0.0 Il0LE $ .0.7071068 0.0 0.0 ll0LE 6 0.7011068 0.7071068 0.0 ll0LE 4 A0 0.7071068 0.0 il0LE 6 0.7071068 0.7071068 A0 CYLINDER 4 i L4 2 PILO UNIT &

CYLINDER 210.6 2 PILO UNIT 9 CYLINDER 210.6 2P150 CYLINDER 0116 2P1LO fl0LE 7 2.0 0.0 0.0 Il0LE 8 2*10 l'.0 ll0LE 7 0.010 A0 Il0LE 8 -1010 0.0 110LE 7 -10 2*0.0 ^

ll0LE 8 2*.2.0 0.0 ll0LE 7 A0 2.0 A0 fl0LE 8 2PLO 0.0 CYLINDER 4 i LB 2 PILO CUBulD 014P4.0 2P16.0 END GEOAl RL4D ARRAYNUX I NUY I NUZ I FILL 9 END ARRAY READ PLOT TTL 'X.Y SLICE AT Z AflDPOINT, NESTED 110LES' XUL-.0,1 >T1L 8.1 ZUL. I6.0 XLR.8.1 YLR-.0.1 ZLR= I6 UAX=l.0 VDN..l.0 N4X 130 hCile' *..X* END 1TL 'X Y SLICE AT Z MIDPolNT. NESTED ll0LES. UNIT MAP' NCil. **l..X3678 '

Plc. UNIT END END PLOT END DATA END A

> - , - -r- em---- *--r-n-+s, sw., - n e- -

v- -

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e Fil.5.104 ..

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,, SES2 tnt 2EEE ,

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,, 31255111E2 A213 R AAAA32515 A125 ,

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. . ~.... .oce....,,

. s e t .+.e et . . . . E 3133 ,

,, 1313 3 . . . . . . es . g.e. .ee***.** 8 ESEE ,

,, SERAR . . . . . . . 84 ... . ... = . . 33

,, LEESE ,

RMas . . . . - . . . . . . . . . 13 e n e se e*e e . . . . . . . . . . . ,4eeeee ese 33 gagg ,-

gaga . . . . . . . . . . . . ... g esesteeeeeet esteceeeeese

,a, , gana . . . . . . . . . . . . . 3 eseeeeeeeeeeese., eee* . .*eeeeeeeeeeeee 3........... 3 . . . . . . . . , * .

• BEst

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,, gama . ...........g3 e e e e e e e ee e e e e e es... ... . e e e eee e e eee e e e t s 33.. ..... 33g3 ,

asAE R a ta

. . . . . . . . .. .... 3 3 eeeeeeeeeeeeeee

== <* . *=.

• R ese*eeeeeeeese

... eseessesseeeece 33.................... . . . . REAE ,

.e. e ee ** ** es ee e e

• 5 . . * * . . . . . .. EEEE ,

,, ta EE ..*..e .~ . . 55 seeeeeeeeeet . . ee t * ** eee e ee e e s II .... . . . .. ,

g333

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,, 335 . . . . . . . . . ES . . . - ~ SJ . ~ . . . . . . EEX ,

,, E t ti R52515&E83 EE ee... eet. ,,ee *. *. EA

• * . + . . 1AEERIERAR E3.13 ,

,, sta IRSAF RAE8 53 .... s e e .. e o s ...e o e ..=. ... 33 3313 33333 333 ,

,, 352 EAR ese 112 85 . . . . . *a 14 RSE , 808 Ea3 555 ,

,, s ni Bat **e Es as .. . + E8 1A ..eet ans 333 ,

,, .33 EEE .. 32 BB . . eee 11 55

,, RA2

.. 332 355 ,

As . . .... .... 12 812 **e ISE SE .. ... 32 Ett - ,

18A3 Ra t 33 e .unee6 4oose . .. e e s . . . .

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13 m e.4 8. et 53 1 ERA 11212 R3 . . . + . .44.. Se ce . . . . 51 3E2 ,

,, 3 8J 52 3

.. .. * . . . . . 5 -

• • • • • • o*,

... EA man ,

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see eeesseeeeeees 33 I

3333 ,

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,, EIA

,, E e

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• s e e e s e 3 5 ... . ... . .... .. .-+ .53 e ***e c e s e *

• e e s s e......s o s e e e e e e e e e e e e e A RAR , '

ERS 2 eeeeeeeeeeeeese . 04 s e e e e e e e e e e e e e 33.............E5 e ee e eeee e ee e ee e e . . . . . ee e e e ee eee e ee e t 3 gang 333 ,

,, g ee ee e e e e e ee ee e s *_ seeeeeeeeeeeee 31 easeeeeeeeeeee anAE 33 ** e e s e ee e ee ee , ese essesesseeos EA . . ... .........

a .. . . . . . . . . . + 3 eesseeeeeose e seeeeeeeeeeesse I ese. . esseeeee*o**e EE asma R A RS Era 3 **eesesee., seeeeees 12 . . . . . . . . . . . 3a esseseee . eeeeeeeen s Ex3 ,

,, 33 3 1A . . ... . . . . . 3

.. . . . . . . . . . 3 .. , . g .. 13 333 ,

,, EAS RE ......es,....ee, se ...s 53 112121118 EJ

.......et.. te se...+. 55 ARE ,

SEER EE .~. .o# 4.. e e s .. . . e e s . .. . .. EA 111A2 RA&&R AS .. ....ees ..w ese ...c o e.* ..w R2 RARA ,

,, gas 15 .. .. . . AN 125 ete.. ESA S3

.. * .o RE ass ,

333 321 . . . . , 3A BA ese . , 13 0.3- . . . . . . . . , 333 353 ,

,, 512 EEJ ***. EA SJ . 52 * **e.. 242 ESA ,

I 124 813 eee . . RAI At . . . . . . . . . ++...AE22 113 . . e ee + t 514 555 ,

112 55212- E RAS EA .~. .

• e t .. . e e s . . . . ..eet 1112 .

32158 518 ,

SAIA 533 RAERRAA112 Eg EX .. .**e e ** ese . . . . 32 ..e+.* SS R215At1144 3E12 ,

. . . . . 31 . . . . . . . 3 42

,, - Ali . . . . . . . . . . . . . Et e e e e'e se * *se . . , . , ... .

s . . . , .. eesecesee 33 ..: 333 ,.

,, 3333 . . . . . , . . . . . . 13 eeeeeese . . .eee . . , esseeeeegese 33 .e.* . . . . . . . . . RAAB ,

,, **......+=+2 eeeeeeeeeeeeet eeeeeeeeeeeese S E A3 .. .4. 3__ 3554

,, 3212 ...........w...53 eseesseeeeeeece . .. ***eeeeeee***e* 9, 25.. 1134 -

,, gaan .....33 ese eeeeee eeeeeee . ......eesseeeeeeeeee ee 33......w. ...m., 3113 ,

,, gaat e ..e gs emee see** eseece ..... eteoeeeeeeeeeee 13 _ ,

. . . . . . . . . . . 3115 asas 3 eeeeeeeeeeeeeet e ee** e sse ee ee os 3.....* E ERA .. ,

5135 . ...........-E ee***oet e*e4 . . . eos , e***eeeeeste E -.... 3113 ,

8252 85 o******** . ..eto****** 13 ....* 1813 ,

,, 15212 m. 32 . ... . . . 51 -*.w. ESAAS - ,

,, Ra13 ......os.....e.,,..ee 3 . . . , . . 3 t a ta ,

3313 3 ..... es e . . .s ee ... e ee . 3 t agg ,

528EI R2 . . 15 Ellia ,

AAA A AS &a .. . . . . . . 13 R1833A , .

SARAS EE . . ees . . , RE E141E ,

32EEEE ERA .ooe. E14 121155 ,

315132 &R&B ERAS 181113

,, 5A12355B EA2151213 523s m a a 5 .,

,, 352A11332 122111113 ,

,, 454AA1145AAE18 I!111313 a n a t1E ,

3RESA AAA AS1 Ale n a s e g13e s s a e sag 33 .

gas a n e aggag ,

Fig. Fil.5e53. Mixture map of nested holes problem t

B., 5&lCS At 8 ElBPO1DT, 558T56 30&98 sult tas gett ma8 fe et 1 a 3 4 5 6 , 9 .

STaach 4 . E S 4 , 8 OTSt&&& STS?dN C90a33taates Amts. 6 9 EmAA v 4. 699995 e 94 fn 48 4.9 31sAse 4.494004 69 Sale. 4.0 SmA2 e 1. 4 09 54G + G ,

t ,43 La9T 60850 t se?-

C9OS8 35ATS4 C00R48patSS 3 4. 9 4640 + S9 0.81968 4 6 ~

T 95 919 9840

• G9 3 9 98 900'e83 S,0494B 4, tates *S3 9 hat 8 9 AJ ta q poes t eactoe8 s -

3 4.6 ,.00044 y .t .44494

. .... 4...9

. ,. -. ,,, .6 ......... . . . . . .i....... -

Fig. Fil 5.54. Plot data for unit map of nested holes "fM. f.e.- w .c 7 v- %g,..?rt .iw$ s'- .f .W'? 1 .r 't ~g'w.gy g yg--y, w. w vg

• v .- . y 9 -ryg--- v t.wwIf

. . . . . -. - . =~ - . . -

quelq Aq 6 !!un puu ',g.: Aq g 1!un ',L,~ Aq t r!un ',9, Aq -

j

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Fil.5.106 1

EXAMPLE 7. LARGE STORAGE ARRAY a

.- - The storage array described in Sect. Fil.5.6.3 and Fig. Fil.5.15 is such a sparse array that the mixture map had to' be very large in order to show the detail of the shelves and uranium buttons. The -

I'

- mixture maps for this configuration were not presented in Sect. Fil.5.6.3 but the data description was listed so the user could generate them. It may be useful to generate a unit map for'this kind of prob-lem. The data description for generating unit maps for this storage: array is given below. The unit I maps have been intentionally distorted by restricting the x direction which extends from 624.84 cm to j

-30.48 cm to 60 lines. The 'z direction which extends from 10.0 cm 1o 196.0 cm is printed in 60 - ,

l

characters. Thus the x direction is considerably compressed.

The plot data and unit map for an x z slice through the array at y=30.48 cm is given in Figs. Fil.5.56 and Fil.5.57. This unit map was created with r across the page and x down the page. .

Thus, the unit map shows five rows of shelves in the x direction represented by l's foi Unit I with the aisles represented by 6's for Unit 6. The borders of Unit 7's are part of the concrete floor, walls, and l ceilings.

\-

....m....a.....,..-.....-

.=

: : : : : :

=,.= =:,:::::

f _..;

- .  ! . ..::::. .l . . .

. 1. .:.:::::.::.

!.".l,' !a!..

{ . . . . . . . . . . .m......... .m._.........

l p

i. - Fig. Fil.5.56. Plot data for x-z slice of storage array j ,

i 4

l F

. , , . . ~ - - -

-- ~ .___.,,.v.sy . . . . . ....m , , , _ . , , . ,,---.--.,.m., .,, , ,r..g r.,,.- y

1

- 1

- Ill 195.l(37 .i 1

l i

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,. 1

,,,,, 9 9 9 9 9 414 t 16119 9 91919 9 ! t ,,,,  !

.. ,,,,, t i t t t 191 t i t t t t t t t t t t t t t t l e t f l

,,,,,51999,119t 19 9 99,11,1119991996699918,t 69699196 t 191119t 9 9111, i, t l ie 619t t t ttt 1411, t t t t t tt t tt i,9,111,,,,

t t t t t ,,,,

, ,9,,

, , l.t.t.t.t .t.t .t .t.19 9 4 t.i.t .t .t.f .i.t.e.l.t .t .t .t.t.t .t.t.t.t .t.t .t.t.t .t .t.t.i .l .l.e.t.e

, , , - .t .t.t .t j

,,9,........................................................

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, , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,,9 .........,,,,,-

,,,,t,...................................................

,,,,..................................................,9t-f,,,.,...................................................,...,.

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,,,,,t i t t f i t t it i f t t t t t t t t t t t t t t t e l t t t t t t t t t t t t t t lit it t l t,,,,

8

,8,,,9 t t t ti t t e t s t e lt t t t le t 1,t tt ttttt sf tt iet te tte19lltt i,ttt tt tt tt lif t t tf lit illiett ttl,,,, $ ,,,,

,1.,,1116 t i t 19 0 t i t t t t t t t s 5.,., ..8 9.t .e .t .t .e .t.t .i .l .t.i.t.t .t.t.t.t .t.t .i.l.l.i.t.t.t.t .t.i.t.t .l .i.t.t.l.i.t.t.t.t .i .l .i .t .i .t .t .t.i , f , ,

,9,,

><.....................................................t..

9,,,,,t....................................................,.,.

15,9,......................................................,

, , , . . .................................................,t,6,

.f.,144,...........................................,.......,,,

8 918 9 0 5 t $ 16 91919 9 9 9 6101119 919 9 9 4 9 4 9 9 6119 41 91199.

,,,,,919 t it t lt t tit t t t t t t t t t t t t t t t t it i t i t t t t t t t t t t t tillt e ,,,,

,,,,,ti t t t tli t t t t t t t t t t t t t t t t t t t t t t t t t tt t t t t t t t t t t tt t tt t t,,,

,,,,, t i t tt tt tt tt tt ttt tt tt tt tiill ll t est tt tt tt tt tf ili e t tPt it tt ttt tt tt tt t t tt tt tt ttttt tilit t 11it ti titit t t t tti,t ,9,,,

,,,,.t ,,

,,,,0......................................................,.

, , , , ,t.it. t. t. t. t. t. t. t. t. e. t. t. t. t. t. t. t. 19. .t .t .i .t .t .t .t .t14. .9 .9 .9 .9 .9 .9 .919. .8 .t .0 .0 .9 .t16116. . . . .,,. . . . . . . , . .

,,,,,ti t ill t a tillli t lt t illlllit t ,t i t t t t t t i t t itit t t t t t t t t ..,

,,,,,t t t t t t t t t t t t t t t t16 t : 4 6 t t t t t t t t t t t t t t t t t t t t t t t t tt tl e ,,,,

,,,,,, t i,,t t t ,,

,e t, ,, t, s,li,t

, ,t, t t,,,t ,s,,,, t y t, t e e t ,t ,r ,

,,,,, e t ,,,

t t t ,i , t ,t ,,,

t t t ,t , ,i t ,,,,,,,

,t ,t t t t ,t t ,t l e t ,,,

Fig. Fil.5.57 x 7 plot of storage array .

The plot data and unit map for an x.y slice through the shelf are given in Figs. Fil.5I58 and' Fil.5,59. This unit rnap was created with x across the page and y down the page. This shows 5 rows of shelves in the x direction represented by l*s for Unit I and. separated by aisles of 6's for Unit 6, There are two rows of shelves in the y direction represented by l's for Unit I and separated by aisles of 4's for Unit 4. The border of 7's are part of the concrete walls. The x direction (down the page) is -

considerably compressed.

1 f

, r-n

171 1.5.1138-

..,.m..,.mmm....w........,...c....m,

., , a 3 . . . .,

i . . .

.... . .i.

C OO..9 A,.. 3.i .,, C DO .D i .A...,

1 . LE f .

..90 A2.h . . .C .O.. a B . ,,s

+ , .. . .......

Fig. F11.5.58. Plot data for x-y slice of storage array m

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,P.,.,,.,,,.,..,....,.........., .. .

,,.,.......................i.....,.....................ii.................................ii............,

,,,,ii.....................,........................ . . . . . . . . . . . . . . . . . . . ..,

.............,i.ii...............................,,.................................i...............

,,ii,.............................................,

.,.,.,.,................................i............

..,,.i..............................................

..........................iiiii...........i, ,

.,.,................................is..........i.i..,

ii........., , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

,,,,i.............,.,..........ii.i....................iiii.,,

,,,.............ii.i...................................,.

. ,i.i.i.i...........

..........................................iii. .

,ii.,.i.................................i..............,

. , ............ii..........ii.i..........

.. . ,. . .. . ,. . .. . ... ... ... ... ... .. .ii..........................,.

,,iii...............................................,,iii.................................................,

,......................i.i.iii........................... . . . . . . . . . . . . . . . . . ..,. . .

,,,,...........i.................................4...,

,,ii.i.i.........i.ii.....................iii...........

,,,,,.,.......................ii.......................

,,,,,..........ii.i............ . . . . . . ...........iiii...........ii, Fig. Fi1.5.59. x-y plot of storage array

___.__ __ ._ ___. _ -'---- -- -- -- - ___,____.m_

~ . . . _ . _. . - - - -. - - - -_ - .

F11.5.109 FI1.5.10 RESTART CAPAlilLITIES Restart data can be written and used for restarting a problem. This type of data is saved by speci-fying a file definition card in the job control language on the unit associated with parameter WRS-when it is written, and RST= when it is read. Most input data can be changed only if the problem is restarted with the first generation. Ilowever, certain parameter data can be changed if the problem is restarted at a generation greater than one.

Parameters that can be changed when a problem is restarted at a generation greater than one include: RND , TME , THA =, GEN , RES., LNG., BEG =, AMX , XAP=, XSI , XS2 ,

PKI , PID , CKU., CKP=, CKil , CKA , FMU., FMP , FMil , FM A., BUG , TRK ,

PWT , PGM , RUN , PLT , NB8 , NL8=, and PAX . All the logical unit numbers can be changed.

If NSK- is changed, it will cause the fluxes, fission densities, leakage, absorptions, and fissions to be incorrect.

FLX =, FDN , FAR , MKU , MKP , MKil- and MKA- can be changed subject to the follow-ing restrictions:

1. If the original problem specified YES, and the restarted problem specifies NO, the data will be calculated but not printed. A warning message will be printed.

2. If the original problem specified NO and the restarted problem specifies YES, an error message is printed and the problem is terminated.

The parameters RUN- and PLT. differ from other parameters because they can be set in the parameter data and overridden in the plot data. Their values are stored in a common block that is writ-ten out if a problem is to be restarted. Therefore, when a problem is run, the value entered in the plot data will override the value that was entered in the parameter data. Ilowever, if the problem is re-started, the value from the restart file will be used unless it is overridden by entering additional data, if WRS. is defined in the parameter data and RES- is not entered, a full restart data file is not written. The input data are written on the restart data file but the calculated data are not. When the restart data file is written in this manner, it can only be used to restart a problem at the first genera-tion. Any desired data can be overridden when a problem is restarted at the first generation. This is accomplished by reading in the desired data.

To write a complete restart data file, both WRS- and RES- must be specified in the parameter data. flowever, WRS- is defaulted to 35 if a value greater then zero is entered for RES . In this case, a file definition card for Unit 35 must be supplied by the user in rader to save the restart data.

A problem that is restarted can also write a restart data file. These data are written on the same data file if no entry for WRS- is made in the parameter data, it can be written on a different unit if WRS- is so specified in the parameter data and the proper file definition card is included in the job control language. If a restarted problem does not have RES-a specified in t6 parameter data, it will continue writing calculated restart data. Therefore, the user can re 'a long problem a little bit at a time by allowing the restarted problem to write restart data and then restarting the problem with those data. This can be done in sequence until the desired number of generations have been completed.

4

. - - .m , - , , , . . ~-m -,--

r. v e , --. - w,-,- . w

.-_ - - - . .~ . ~ . - --- _ - . . - ~ ~ . .

'Fil.5.110 For example, consider a problem that is to run 500,000 histories (500 generations of 1000 histories _ ,

per generation) and the amount of computer time available at any given time is quite limited. On the first pass, GEN-500 NPG-1000 RES-500 WRS-35 should be included in the parameter data and a unit specification for Unit 35 should be included in the job control language when the problem is run.

Note that 35 is an arbitrary number chosen by the user. KENO V will automatically pull the job before it runs out of time or I/O's. A restart data file will be written on Unit 35 for the last generation that was completed. If the user wishes to restart the problem by reading the data from Unit 35 and writing a new restart file on the same unit, the parameter data for the second and all subsequent passes would be: READ PARAM 11EG-500 RST-35 FND PARAM.

The random sequence can be changed when a problem is restarted by entering a different random number in the parameter data. The starting random number is acceptable for changing the random sequence of a problem that is to be restarted at a generation greater than one.

Parameter data can be changed by entering new values for the desired options. This has the effect of inputting additional data within the parameter data block as explained in Sect. Fil.5.3. However, all other data blocks that are to be changed must be entered as an entire data block and will completely replace that data block from the restart problem. When a problem is restarted and some of the data are overridden, the original restart data blocks are retained on the unit defined by WRS=, if it is the same as the unit defined by RST . If the unit number associated with WRS- is different from the unit number associated with RST=, the resultant data blocks are written on the unit number associated with WRS . For example, if the original problem is a single unit problem with RST-95 and WRS-95, and an array data block is entered to change it to an array problem, the original single unit problem data blocks remain on Unit 95. Ilowever, if the single unit problem is restarted with RST-95 and WRS-96. and an array data block is entered to change the problem to an array problem, the origi.

nal single unit data blocks remain on Unit 95 and the resultant array problem data blocks are retained on Unit 96.

When a problem is restarted, the only way to change data in a data block is to reenter a new data block. For example, if in the original problem an array data block was entered as: READ ARRAY NUX=Il NUY-5 NUZ-3 END ARRAY and the problem is to be restarted at the f;rst generation as an lix5x6 array, the following data block must be entered: READ ARRAY NUX-Il NUY-5 NUZ-6 END ARRAY.

Section Fil.2.6 contains some information pertaining to the restart capability. Other information may be found in Sect. Fil.4.3. The structure of the restart file is listed in Table Fil.5.2, and the variables referenced in that table are listed in Table Fil.5.3.

Fil,5.Il RANDOM SEQUENCE The random number package utilized by KENO V always starts with the same seed and thus always reproduces the same sequence of random numbers. The current random number is printed at various places in the KENO V printout, and any of them except the one printed in the parameter table j can be used to activate a different random sequence. The user can rerun a problem with a different random sequence by simply entering a hexidecimal random number, other than the. starting random number, in the parameter data. The last digit of the random number should always be an odd number. <

For example, by entering RND- A10Cl893E6D5 in the parameter data, the problem will be run with a different random sequence.

_ . - - . . . - , , - . - . _ - . _ - , - - . - , . - - . ~ . - . ..- - - --.._,.---- -.-- .

1 FI LS.ll i-l Table Fil.5.2. Structure of RESTART file l Record number Contents (1) TITLE (20), NBA, NPB, NSKIP, NRSTRT, NBANK, NFBNK, NXBNK, NXFBK, NUMX1D, TMAX, l'i TCH, RNDNUM, LOG'l(36)

(This record contains the title and parameter data.)

(2) MT(LMT) LMT - 5 + NUMXtD (This record contains the identifiers of the 1-D cross-section arrays.)

(3 to NUMPT+2) NDX - 1, NUMPT NUMPT - 11 (a) NDX,NREC (This record contains the index for each type of data and the number of records of data associated with each type of data.)

(b) NREC - 1 records of data (These records contain the data associated with the specified type of data.)

NDX - 1 (geometry data)

(bt) LLNGTil, KMAX, KREFM, NGBLU, NBOXT,MAXMIX, .

M AXIMP, NUM HOL, NUCOM, EXRFL, LFIL, LFIL, LFIL (b2) M AT(KREFM), IMP (KREFM), FGEOM(KREFM),

IGEOM(KREFM), XX(7,KREFM), KBNDSl(NBOXT),

KBNDS2(N BOXT), IFil(KREFM ), ILH(KREFM),

KHOLE(NUMHOL), LHOLU(NUMHOL), HOLX(NUM HOL),

HOLY (NUMHOL), HOLZ(NUMHOL), ICOMC(NBOXT),

4 UCOMNT(33,NUCOM)

NDX - 2 (array or unit orientation data)

(bi) LLNGTH, NGLOBL, MAXARA, NACOM, LSGUN, MBOX, LFIL, LFIL -

(b2) NBXMAX(M AX ARA), NBYMAX(M AXARA), NBZM AX(MAXARA),

ITYPE(M AX ARA), LPT(M AXARA), LNG (M AXARA),

ICOMA(M AXARA), ACOMNT(33,NACOM)

' I-1,MAXARA (The following records are written for each array if multiple units are entered in the geometry data.)

(b3) IF (LPT(1).GT.0) LBA(NBXM AX(1),NBYM AX(1),NBZM AX(1))

NDX - 3 (mixing table data)

(bl) LLNGTH, NMIX, NSCT, MIX, MIXT, NPL (b2) MIXTUR(NMIX), NUC(NMIX), DEN (NMIX)

NDX - 4 (extra data)

.-. _. .._=. . . . .- . . . . _ _-. . . - . - . . . _ - . . ~.

r Fil.5.ll2 Table i?ll.5.2 (continued)

. t Record number Contents (bl) LLNGTil (b2) D(LLNGTil)

NDX - 5 (weighting frrction by energy group and importance reg.)

(bl) LLNGTil, NIMP (b2) WTAVG(NGP N MP)

NDX - ti(start data)

I (bl) LLNGTil. NTYPST, TFX, TFY,TFZ, NBXS NBYS, NBZS KFIS, LFIN, NBOXST, FRACT, F'SVOL, XSM, XSP, .

YSM, YSP, ZSM, ZSP, RFLKEY, LPRT6, LPSTP, LFIL (b2) IF (NTYPST .EQ. 6) X(NPB), Y(NPB), Z(NPB),

NBX(NPB), NBY(NPB), NBZ(NPB)-

NDX - 7 (albedo data)

(b1) LLNGTit, NALB, NANO, NG, INTR (6) ,RNAMES(2,6),

IDALB(6), NBXL(6), LNXX IF (NALB .GT. 0)

(b2) NABS (3 NALB), LABS (3,NALB) <

(b3) MAL (3 NANG,NG)

(b4) EALB(NG+ 1) (group boundaries) 1 - 1,NALB (b5(i)) PLIM(NANG), CPOL(NANG), SPOL(NANG)

(b6(i)) ALB(LENG) (LENG is the length of the albedos

j. for a given angle.)

1 (b7(i)) A(LENG,NANG)

. NDX - 8 (mixed cross sections) l l (bt) LLNGTil, MATT, NGP, NSCT l

(b2) LXS(M ANG, MATT) MANG - 2*NSCT + 4 1

, .,.--.,,r. . , _ . - . . . _ . . . . . - . -. ... ._ , . .-- . _ _ _ .-

_.._____m.

Fil.$.ll3 Table Fil.5.2 (continued)  :

Record number Contents 1 - 1, M ATT for each existing mixture (b3(i))ID'$0) the rnixture information record (b4(i)) X1D(NNID,NGP+ 1) NNID - ID(28) no. of I D's (b5(i)) MWA(3 NGP)

(b6(i)) P0(LNG) LNG - MWA(2,NGP)

J-1.NSCT (b7(ij)) ANG(LNG). ,

(b8(ij)) PRB(LNG) '

NDX - 9 (energies and inverse *clocities) ,

(bl) LLNGTil r

(b2) E(FGP+ 1), VINV(NGP)

NDX - 10 (plot data)

(bl) LLNGTil, NUMPLT 1 - 1, NUMPLT (b2(i)) XL, YL, ZL, XR, YR, ZR, VX, VY, VZ, UX, UY, UZ, DELV, DELU, NV, NU, LPIC, PTITL(33),

TABLE (59) l-NDX - 11 (biasing data) l-(bt) LLNGTil, NUMIDS, NCS, NTSETS i

IF ((NUMIDS + NCS).GT,0),

(b2) ID(NUMlbS), IBGN(NUMIDS), IEND(NUMIDQ ,

L WTTITL(3,NUMIDS), NCID(NCS), NCSETS(NCS), a l

l CRDITL(3,NCS), NCTilK(NTSETS), NUMINC(NTSETS),

NGPWTS(NTSETS), IPTWT(NTSETS)

! - 1, NCS J -1 NSETS(l) 1 (b3(ij)) WTAVG(NGPWTS(j,i),NUMINC(j,i))

(14 to END) calculated data as listed below

- . . * - . ~ . , - - . . . , ,.,+ < . * , . . - . . -, , <- + y - - - , .2-..--'.-,-.,,

Fi1.5.114 Table Fil.$.2 (continued)

Record number Contents (a) IGEN, RND, NPD, NGP, KMAX, LBANK NBANK, LIF(50),  !

LOJIC* l(36), EFFK(IG EN)

(This record contains parameter data, COMMON /LIFETM/

part of COMMON / LOGIC / and k-effectives by generation.)

(b) NUBANK(f. BANK,NBANK) r (c)IF(LOJIC(4)) FISDEN(KMAX)

(if fission densities are calculated, the fission densities aie written on the restart file.)

(d) IF(LOJIC(10))

TP(M ATDIM,M ATDIM,3), SNP(M Al l4M. SP(M ATDIM )

(if mattin data by position are calculated, the matrix by position data are written on the restart file.)

(c) IF(LOJIC(7))  !

TU(NDOXT, NBOXT,3), SNU(NBOXT), SU(N 40XT)

(if matrix data by unit are calculated, the matrix by unit data are written on the testart file.)

(f) IF(LOJIC(13))

Til(NUMilOL,NUMHOL,3), SNH(NUMilOL), Sil(NU., .40L)

(if matrix data by hole are calculated, the matrix by hole da.a are written on thc restart file.)

(g) !F(LOJIC(17))

TA(NUM ARA,NUM ARA,3), SNA(NUM ARA), S A(NUM A RA)

(!f matrix data by array are calculated, the matrix by a ray data are written on the restart file.)

(h) I to NGP (the following records are written for each energy grov,.

(hl) !GPOUP, FLEAK(3)

(h2) FM ABS (LREO,3), FMFIS(LREG,3)

(h3) IF(LO.IIC(3)) FLOX(KMAX,3)

Repeat (a through h) until LOJIC(34) is TRUE, i.e , until the last generation is completed.

l l

l l

l v L

l L. . . _ _ ~ ___ .. - __

- - - - - - - - . _ . - _ - - - - _ _ - - - - ~ . . _ - . _ . - -

Fil.5.Il5 i t

Table Fil.$.3. Key of RLSTART file variables TITLE 80 Character KENO problem title NilA Number of generations in the KENO problem NPil Number of histories per generation NSKIP Number of Fenerations to be skipped in averaFi ng k-effecthe NRSTRT Number of generations between writing restart data NilANK Nurnber of feitions in the neutron bank N1 llNL Number of positions in the fission bank NXilNh Number of extra entries in the neutron bank NXiIIK Nember of extra entries in the fission bank  !

NUMX1D Number of extra 1 D cross sections TMAX Time allowed to execute the problem 1111C11 Time allowed for each generation RNDNUM Random number with which the problem will be started LOG COMMON / LOGIC /

LMT Number of I D crosesection identifiers. LMT - 5 + NUMX1D MT Array containing the 1 D crosesection identifiers NUMPT Number of kinds of data that are written on the restart file NDX Index for the type of data NRLC Number of records for the specified type of data NDX - 1 geometry data LLNGTil The length of record b2 KMAX Number of geometry regions used

, KRiil M Number of geometry cards read in the geometry data

! NilOX Largest unit or boxtype number in the geometry data NBOXT N il O X 4 the number extra units generated by KENO M AXMIX Largest mixture number encountered in the geometry data MAXIMP Largest biasing number encountered in the geometry data l N U M ilO L Number of holes in the geometry data EXRFL logical flag. Value is TRUE if a reflector is present MilOX legical flag Value is TRUE if multiple units are entered I.FIL logical'l blank variable used to pad to full word boundary l MAT Array containing the mixtures used in the geometry IMP Array containing the bias ID's used in the geometry iGEOM Array containing the geometty words used in the geometry IGEOM Array containing the shape identifiers used in the geometry XX Array of geometry dimensions KilNDS1 Array of the first geometry region number in each unit KilNDS2 Array of the last geometry region number in each unit ,

11;11 First hole number encountered in each geometry region ILil Last hole number encountered in each geometry region KilOLE Region number that contains the hole LilOLU Unit that is placed in the hole llOLX X coordinate of the origin of the unit in the hole with respect to the unit that contains the hole ,

llOLY Y coordinate of the onFi n of the unit in the hole with respect to the unit that contains the hole l llOLZ Z coordinate of the origin of the unit in the hole with respect to the unit that contains the hole NUCOM- Number of geometry comments UCOM NT Comments

Fil 5.116 .

s

~

~

Table Fil.5.3 (continued)

NDX - 2 array or unit or.cntation data LLNGTil length of the b2 record NGLOllL Global array number MAXARA Largeu array number encountered in the array data LSGUN Logical flag. Value is TRUE if there is no array present 1 LFIL Logical'1 blank variable used to pad to full word boundary NilXMAX Number of units in the X direction of each array i N!!YMAX Number of units in the Y direction of each array NBZMAX Number of units in the Z direction of each array '

ITYPE Pitch indicator, I for square pitched arrays LPT Pointer to locate the beginning of each unit orientation array LNG Length of each unit orientation array LilA Contains the unit orientation arrays for all arrays NACOM Number of array corntnents  ;

ACOMNT Comments NDX - 3 mixing table data LLNGTil Length of b2 record NMIX Number of entries in the mixing table NSCT Number of scattering angles MIX Number of different mixtures to be mixed  ;

MIXT Largest mixture number to be mixed NPL Order of Legendre coefficients + 1 PilXS Cross section message cutoff value MIXTUR Array of Mixture numbers used in the mixing table NUM' Array of the nuclide ID numbers used in the mix:ng table DEN Array of the number densities used in the mixing table NDX - 4 cxtra data t

LLNGTil Length of b2 record i LENGTil D(LENGTil) is the data contained in the S2 record NDX=$ weighting function LLNGTil Length of b2 record NIMP Number of biasing regions WTAVG Average weight by energy group and basing region NDX - 6 start data (initial source distribution)

LLNGTil Lengt.. c' b2 record NTYPST Start tyy to define the initial source distribution -

TFX X coordinate of neutron starting point ,

TFY Y coordinate of neutron starting point TFZ Z coordinate of neutron starting point NBXS X index of unit's position in the global array NBYS Y index of unit's position in the global array NBZS - Z index of unit's position in the global array  ;

i KFIS Mixture whose fission spectrum is used for initial source LFIN ' Last neutron to be started at the specified point NBOXST Unit in which neutrons will be started FRACT Fraction of initial source to be started as a spike

i

! I:11.3.I 17 Table I ll.5 3 (continued)

I'ISVOL I raction of global system that contains fissile material XShi -X dimension of cuhoid in ahich neutrons will be started XSP + X dimension of cuboid in which neutrons will be started YShi Y dimension of cuboid in which neutrons will be started YSP 4 Y dimension of cuboid in which neutrons will be started ZShi Z dirnension of cuboid in which neutrons will be started ZSP 4 Z dimension of cuboid in which neutrons will be started Iti llEY logical variable. Set TRUli if neutrons can be started in reflectcr I.PR16 I orical variable. Set TRUE to print start type 6 data LPS1P logical variable. Set TRUE to print initial source points 1.1 11. Logical *1 blank variable used to pad to full word boundary NPil Number of histories per generation _

X X coordinate of neutron starting point for start type 6 Y Y coordinate of neutron starting point for start type 6 Z Z coordinate of neutron starting point for start type 6 NilX X index of unit's position in the global array for start type 6 NilY Y index of unit's position in the global array for start type 6 Nilz Z index of unit's position in the global array for start type 6 NDX - 7 albedo data LLNGTil Length of b2 record NAlli Number of different differential albedos to be used NANG Number of angles available in the albedo function NG Number of energy groups available in the albedo function INTR Type of boundary condition for each face RNAh1ES Name of boundary condition ,

IDAllt Index to the correct set of albedo data NilXL Specifies the f ace where the history will reenter LNXX logical flag. Set TRUE for either specular or differential reflection NAllS Pointers into the albedo data for each albedo used LAllS Length of the albedo data for each albedo used h1AL Pointer array for albedos EAlli Energy boundaries for albedos PLlhi incident polar angle bins CPOL Cosine of returning polar angle SPOL Sine of returning polar angle ALil Probabilities for the returning energy group ALil Probabilities for the returning angle LENG Length of albedo data for a given angle NDX - 8 mixed crou sections LLNGTil Length of b2 record h1ATI Number of mixtures used in the problem NGP Number of energy groups from the cross section file NSCT Number of scattering anF les LXS 1ength of each cross section set htANG 2* NSCT + 4 ID llead record from mixed cross section file XID l D cross sections

t h

Fil.$.ll8 Table Fil.$.3 (continued) ,

l NNID Number of 1 D cross sections (ID(28))

MWA Pointer array for cross sections P0 Group-to group transfer probabilities ANG Scattering angles PRD Probabilities for scattering at angle ANG LNG Length of the P0 arrays NDX - 9 energies and inverse velocities LLNGTil Length of b2 record NGP Number of energy groups E Energy group bounds VINV Inverse velocities NDX - 10 plot data LLNGTil Length of b2 record NUMPLT Number of plots to be generated XL X coordinate of the upper left corner of the plot YL Y coordinate of the upper left corner of the plot ZL Z coordinate of the upper left corner of the plot XR X coordinate of the lower right corner of the plot YR Y coordinate of the lower right corner of the plot ZR Z coordinate of the lower right corner of the plot VX X component of the direction cosine for the across axis of the plot VY Y component of the direction cosine for the across axis of the plot VZ Z component of the direction cosir.c for the across axis of the plot UX X component of the direction cosine for the down axis of the plot UY Y component of the direction cosine for the down axis of the plot UZ Z component of the direction cosine for the down axis of the plot DELY Horizontal spacing between points on tbc plot DELU Vertical spacing between points on the plot NV Number of characters across the plot NU Number of characters down the plot LP!C Plot type indicator. LPIC. I mhture, LPIC-2 unit, LPIC-3 bias ID PTITL Plot title,80 characters TABLE Characters used in plot,59 characters NDX - 11 biasing data LLNGTH 1.cngth of b2 record NUMIDS Number of bias ID's requested NCS Number of bias ID's entered from cards NTSETS Total number of group structures for all ID's ID ID number or set of weights to be read from WTS file IBGN Beginning importance region number assigned to ID LEND Ending importance region number assigned to ID WTTITL Title associated with the ID j NCID ID to be read from cards l--

l

, - - y -,m- ., , ,,_ - .,...., ,_ ,...-.+_.,-~~r -w a ..v- . .-. , _ .--. . . . , 4- .,-,r,,y. ..w,-i, v--r-

FI L5.Il9 Table Fil.5.3 (continued)

NCSETS Number of group structures to be read from cards CRDTTL Title anociated with the ID read from cards NCTilK Thickness gr increment from cards NUMINC Number of increments from cards NGPWTS Number of energy groups for this 6ct of weights IPTWT Pointer into the weights from cards WTAVG Weighting function by energy group and importance region fol!N Generation for which this set of restart data was written RND 1.ast random number that wari used NPil Nun 3ber of generations NGP Number of histories per generation KMAX Number of geornetry regions used i IIA N K Number of positions per neutron in the neutron bank NilANK Number of positions in the neutron bank LIF An array equivalenced to COMMON /LIFETM/

LOJIC An array equivalenced to COMMON / LOGIC /

lil FK Array containing k effectives by generation NUllANK The neutron bank, NilANK by LilANK '

FISDEN Array containing the fission densities TP Fission production matrix by array position SNP Eigenvector of the fission production matrix by array paition SP Source vector by array Faition TU Fission production rnatrix by unit SNU Eigenvector of the fission production matrix by unit SU Source vector by unit Til Fission production matrix by hole SNil Eigenvector of the fission production matrix by hole Sil Source vector by hole '

TA Fission production matrix by array SNA Eigenvector of the fission production matriz by array SA Source vector by array IGROUP Current energy group FLEAK teakage fraction FMAllS Absorption fraction FMFIS Total fission production FLUX Flux LOJIC(4) Key indicating whether to calculate fission densities Specified by entering FDN- in the parameter data LOJIC(10) Key indicating whether to calculate matrix data by position Specified by entering MKP- in the parameter data LOJIC(7) Key indicating whether to calculate matrix data by unit Specified by entering MKU- in the parameter data LOJIC(13) Key indicating whether to calculate ruatrix data by hole Specified by entering MKil. In the parameter data LOJIC(17) Key indicating wheiber to calculate matrix data by array Specified by entering MKA- in the parameter data LOJIC(3) Key indicating whether to calculate fluxes Specified by entering FLX= in the parameter data

._____m..._._____________- _ _ _ _ _ _ _ . _ _ _ _ ._

Fil $.120

[

Fil.5.12 M ATRIX K EFITCilVE Matrix k effective calcu!ations provide an alternate method of calculating the k-effective of the sys-tem. Cofactor k-effectives and source vectors are additional information that can be provided when the matrix k-effective is calculated. The necessary source and fission weiF ht data are collected during the neutron tracking procedure in subroutine TRACK. This information is converted to a FISSION PRO.

DUCTION M ATRIX which is the number of next generation neutrons produced at J by a neutron born at 1. The principal eiFenvalue of the fission probability matrix is the matrix L-effective. KENO V offers four alternatives when calculating mattin k effective as discussed below:  :

(1) If MKP-Y13 is specified in the parameter data, the fission production matrix is collected by atra) position of position index. The pmition index is used to reference a given location in a three dimensional lattice. Ior a 2x2x2 array there are eight unique position indices as shown below.

l'OSillON POSITION INDEX X Y Z l I i 1 2 1 1 1 3 1 2 1 4 2 2 1 5 1 1 2 6 2 1 2 7 1 2 2 8 2 2 2 The fission production matrix is the number of next generation neutrons produced at inoca J by a neutron born at index 1. This matrix is used to calculate the matrix k-effective, cofactor k effectives and the source vector by imition index. liccause the size of the fission probability matrix is the square of the array site (for a 4x4x4 array there are 4096 entries), it can use vast amounts of computer memory.

(2) If MKU-YES is specified in the parameter data, the fission production matrix is collected by unit or box type. It is the number of next Feneration neutrons produced in unit or box type J by a neutron born in unit or box type 1. This matrix is used to calculate the matrix k-effective, cofactor k-effectives and source vector by unit or box type.

(3) If MKil-YES is specified in the parameter data, the fission production matrix is collected by hole number. Matrix information can be collected at either the highest hole nesting level (first level of nesting) or the deepest hole nesting level. tillL-YES specifies that the matrix informa-tion will be collected at the first nestinF level. Ily default, the matrix information is collected at the deepest nesting level. The fission production matrix is the number of next generation neu-trons produced in hole J by a neutron born in hole 1. This matrix is used to calculate the matrix k-effective, cofactor k effectives and the source vector by hole.

l (4) If MKA-YES is specified in the parameter data, the fission production matrix is collected by array number. It can be collected at the highest anay level (first level of nesting) or at the deepest array level. IIAL=YES specifies that the matrix information will be collected at the first nesting level. Ily default, the matrix information is collected at the deepest nesting level.

The fission production matrix is the number of next generation neutrons produced in array J by a neutron born in array 1. This matrix is used to calculate the matrix k-effective, cofactor k- I effectives and the source vector by array.

I

I t

I'l l.$,12 6 '

Tic user can simultaneously utilite all methods of calculating the matrit k-effective. 'Ibc results are