Scholars' Mine Masters Theses Student Theses and Dissertations 1969 Nuclear parameter study in one, two, and three dimensions Jan Robert Lojek Follow this and additional works at: https://scholarsmine.mst.edu/masters_theses Part of the Nuclear Engineering Commons Department: Recommended Citation Lojek, Jan Robert, "Nuclear parameter study in one, two, and three dimensions" (1969). Masters Theses. 6963. https://scholarsmine.mst.edu/masters_theses/6963 This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. NUCLEAR PARAMETER STUDY IN ONE, TWO, AND THREE DIMENSIONS BY LfL/!) JAN ROBERT LOJEK J A THESIS submitted to the faculty of THE UNIVERSITY OF MISSOURI ROLLA 155J8Z in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE IN NUCLEAR ENGINEERING . 0 Ro 11 a, Missouri 1969 Approved by 'Zdcd_ ~ (advisor) c '-'i. i i ABSTRACT A parameter study comparing one-, two-, and three-dimensional reactor design analyses was undertaken. Computer programs {codes) were used extensively for the computations and running times on the IBM 360/50 were observed. The values of primary concern were neutron flux shapes, effective multiplication factors, and fuel depletion. Dresden I nuclear power plant with fuel type 1 represents the model reactor. Cross section calculations were performed using the nuclear codes HRG and TEMPEST I 1. FEVER, EXTERMINATOR-2, and FLARE generated the nuclear parameters. iii ACKNOWLEDGMENTS The author wishes to thank Dr. Hichull Kim and Dr. Doyle R. Edwar~ for their advice, encouragement, and assistance in this work. He is also grateful to Dr. T.B. Fowler and Dr. Owen H. Gailer for their assistance in obtaining and using the nuclear computer codes. Recog­ nition is also due the Babcock and Wilcox Company, Purdue University, and Commonwealth Edison Company for use of their computer facilities. The author is also grateful to the Atomic Energy Commission for the financial support received during this endeavor. iv TABLE OF CONTENTS Page ABSTRACT • • • • . • • • • • . • . • • • • • . • • • • • • • • . • • . • . • • • • . • . • . • . • • . • . i i ACKNOWLEDGEMENTS • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • iii TABLE OF CONTENTS • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • i v LIST OF FIGURES •.......••.....••..•...•.•.•.•.•.•......••..•.•.•. vi L I ST 0 F TABLES . • • . • . • • • . • • • • . • . • . • . • . • . • . • . v i i I. INTRODUCTION ••••••••••••••••••••••••••••••••••••••••••••••• II. LITERATURE SURVEY •••••••••••••••••••••••••••••••••••••••••• 2 A. APPLICATIONS AND DISTINCTIONS OF NUCLEAR CODES ••••••••• 2 B. ONE-DIMENSIONAL METHODS 3 c. TWO-DIMENSIONAL METHODS . .............................. 4 D. THREE-DIMENSIONAL METHODS.............................. 6 E. CROSS SECTION CALCULATIONS ••••• ••••••••••••.••••••••••• 7 l. Fast Cross Sections •••••••••••• ••••••••••• •• ••••• •• 7 2. Thermal Cross Sections ............................. 8 Ill. DISCUSSION ••.....•.•....•.•..•.••..•.•....••....•......••.. 9 A. DESCRIPTION OF DRESDEN I REACTOR .. .. .. • •• .. • .. • • .. • • • .. 9 B. INPUT PREPARATION FOR CODES •• ~........ • • • • • • • • • • • • • • • • • 21 1. Cross Section Calculations ••••••••••••••••••••••••• 21 2. One-Dimensional FEVER Code ......................... 28 3. Two-Dimensional EXTERMINATOR-2 Code •••••••••••••••• 30 4. Three-Dimensional FLARE Code ....................... 33 I V • DATA AN D RESULTS • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 3 8 A. CONVERGENCE AND ASSUMPTIONS ............................ 38 B. EXCESS REACTIVITY OVER LIFETIME ........................ 42 C. THERMAL NEUTRON FLUX CORRELATION ••••••••••••••••••••••• 50 v Page D. CONTROL ROD INSERTION COMPARISON ....................... 51 E. POWER DISTRIBUTION STUDY ............................... 54 V. CONCLUSIONS . 62 VI. RECOMMENDATIONS . 64 BIBLIOGRAPHY . 65 APPENDICES . 68 I. COMPUTER PROGRAM TO PUNCH WEIGHTED FEVER CROSS SECTIONS 68 I I. COMPUTER PROGRAM TO PUNCH EXTERMINATOR-2 CROSS SECTIONS FROM FEVER CODE . 72 VITA 77 vi Ll ST OF Fl GURES Figure Page I. Cross Section of Dresden Reactor 12 2. Detailed view of Dresden co re 1at t i ce 13 3. Approximated cylindrical regions of Dresden 15 4. Rectangular region of solution in R-Z plane (EXTERMINATOR GRID) 32 5. Dresden I - quarter core X-Y plane configuration 35 6. Flow chart of operations 39 7. C r i t i ca 1 i ty ~ 1 i fe t i me 45 8. Thermal flux vs distance 53 9. Criticality~ control rod insertion 56 10. Flat control rod pattern 59 I I. Source strengths per element with Figure 10 rod pattern 59 12. Steep slope cone-shaped control rod pattern 60 13. Source strengths per element with Figure 12 rod pattern 60 14. Moderate slope cone-shaped control rod pattern 61 15. Source strengths per element with Figure 14 rod pattern 61 vii LIST OF TABLES Table Page Reactor core description 10 2 Region boundaries 14 3 Initial number densities before startup - 68°F 18 4 Number densities at operating temperatures -entire coolant volume composed of water @500°F 19 5 Number densities at operating temperatures and 1015 psia 20 6 HRG resonance absorption values 25 7 Thermal energy group constants for cold (68°F) core 27 8 Convergence criteria 38 9 keff over reactor life 10 FLARE constants - cold case, Source: Commonwealth Edison 46 II FLARE constants - operating case Source: Commonwealth Edison 47 12 FLARE constants - operating case Source: Combustion Engineering 48 13 keff code differences over reactor life 49 14 Thermal fluxes, collapsed thermal fluxes, and source strengths (normalized) vs radial distance from center of reactor core 52 15 k ff ~control rod insertion at operating beginning of ife 55 AI Fortran source deck listing of weighted FEVER cross section program 69 A2 Sample input data for the punch program in Table AI 70 A3 Sample computer output for input data in Table A2 71 A4 Fortran source deck listing of EXTERMINATOR punch program 73 AS Sample input data for the punch program in Table A4 75 A6 Sample computer output for input data in Table A5 76 I. INTRODUCTION The objective of this investigation is the analysis and comparison of reactor design parameters calculated by one, two, and three-dimen- sional methods. The basic procedure entails selection of a model power reactor and a set of nuclear codes that are capable of calculat- ing neutron cross sections and design parameters in one, two, and three dimensions. Dresden I was chosen as the model reactor since it satis- fied the required criteria and the reactor core description was obtainable. Selection of the codes was based on their ability to execute the desired calculations. However, in some cases, compro- mises had to be made due to computer incompatibility and unavailability ~ of codes. The nuclear codes" adopted include the cross section codes HRG and TEMPEST-I I and the diffusion codes FEVER, EXTERMINATOR-2, and FLARE. Correlation of elapsed computer time and nuclear parameter accuracy is an important area in fuel analysis and design. Industrial concerns are particularly interested in using the fastest and most economical design methods available and at the same time maintaining a suitable level of reliability. Hopefully, this would help alleviate overdesign in power plant and fuel analysis resulting in considerable financial savings. In addition to its direct application to the nuclear industry, the selection of this investigation was complimented by the author•s experi- ence with computer operations. Much valuable experience was also gained by working with and uncierstanding the workings of several nuclear codes. * Discussed in the Literature Survey 2 I I. LITERATURE SURVEY A. APPLICATIONS AND DISTINCTIONS OF NUCLEAR CODES One of the most important tools available for reactor design studies today is the electronic digital computer. With it one is capable of performing sophisticated calculations which aid in optimum core design, isotope change and maximum fuel life determina- tions, and improved safety techniques. The emphasis in this inves- tigation wi I I be placed on criticality and fuel burnup studies. A large commercial power reactor must be economical a5 well as safe. Economy is strongly influenced by the precision with which nuclear and thermal hydraulic parameters can be predicted. The type and accuracy of the fuel burnup analysis are also important. In ( I ) fuel burnup alone there may exist a 10-20% uncertainty in the initial prediction of end of life keff' which results in an added half to a million dollars in the annual fuel cost of operating a 500-MWe plant. However, as the core life increases, the predic- tions may be updated by the operational history of the reactor, lessening the full impact of the initial uncertainty. A feedback system between theoretical approximations and actual results would continually improve the computational methods available. Of primary concern to the reactor purchaser as well as the designer and manufacturer is how temperature, pressure, and time affect the criticality and core power distribution over lifetime. Most studies which incorporate the above analysis can be categorized according to the number of space dimensions which they account for 3 explicity. The