ABSTRACT Title of Document: Flux Maps Obtained from Core Geometry Approximations: Monte Carlo Simulations and Benchmark Measurements for a 250 kW TRIGA Reactor Ali Bellou Mohamed, Doctor of Philosophy, 2009 Directed By: Professor, Mohamad Al-Sheikhly and Professor Emeritus Joseph Silverman, Graduate Program in Nuclear Engineering, Materials Science and Engineering Department Two MCNP models (detailed and approximated) of the University of Maryland Training Reactor were created. The detailed model attempted to simulate the reactor according to engineering specifications while the simplified model eliminated all structural materials above and below the core. Neutron flux spectrum calculations for both models within the core showed that the results obtained from both models agreed within less than 0.5%. It was concluded that reactors equipped with standard TRIGA fuels enriched to 20 percent in uranium-235 can be modeled with all structures above and below the core eliminated entirely from the model without increasing the error due to geometry modeling simplifications of the core. In TRIGA reactors supplied with standard TRIGA fuels enriched to 20 percent in U-235, the graphite reflectors above and below the fuel act as “neutron energy regulators.” Neutrons reflected back into the core through the graphite reflectors quickly become thermalized even if their energies were altered due to the change in materials properties above and below the core. Both MCNP models results agree well with measured data. It was also found that simplification in the target geometry leads to substantial uncertainty in the calculated results. The neutron energy spectrum, thermal flux, and total flux were calculated at the thermal column access plug face; in the pneumatic transfer system rabbit, and on top and bottom sections of the most center fuel element. The thermal flux and the total flux at the thermal column access plug face both agreed with measured data within a 5% uncertainty. The thermal flux, fast flux, and the total flux in the rabbit differ by 18.8%, 35%, and 5.7% respectively, from the measured data. The relatively high uncertainty (in the neutron energy distribution but not the total neutron flux) was attributed to the use of air as the target irradiated inside the rabbit. For such a thin target (15 mg/cm2), a precise neutron balance between reflection and absorption events is difficult to obtain; that will alter the thermal or fast flux values. The contribution of this work to the reactor users is that a virtual reactor model that compared well with experiment is created. Experiments utilizing the reactor experimental facilities (thermal column, through tube, pneumatic transfer system rabbit, and beam ports) can now be optimized before they are executed. The contribution of this work to the research reactor community is that research reactors equipped with standard TRIGA fuels enriched to 20 percent in U-235 can be modeled with core geometry approximations, such as these adopted in this work, without affecting the precision and accuracy of the Monte Carlo calculations. FLUX MAPS OBTAINED FROM CORE GEOMETRY APPROXIMATIONS: MONTE CARLO SIMULATIONS AND BENCHMARK MEASUREMENTS FOR A 250 KW TRIGA REACTOR By Ali Bellou Mohamed Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2009 Advisory Committee: Professor Mohamad Al-Sheikhly, Chair Professor Emeritus Joseph Silverman Professor Mohammad Modarres Professor Gary Pertmer Professor Shapour Azarm © Copyright by Ali Bellou Mohamed 2009 Dedication To My Mother Amna ii Acknowledgements First, I would like offer my sincere gratitude to my advisor Mohamad Al- Sheikhly, Professor and Director of the Radiation Facilities and Nuclear Reactor, for his continued support and guidance for my Ph.D. research, and patience with me throughout the course of this work. Words simply are shy to express my utmost sincere gratitude to my co-advisor Joseph Silverman, Professor Emeritus, for his unconditional support for my research, and in personal matters. Professor Silverman stimulating ideas are always around the corner. Professor Silverman, thank you for every thing. I would like to thank my dissertation committee: Professor Gary Pertmer, Associate Dean, Professor Mohammad Modarres, and Professor Shapour Azarm, for their encouragement, insightful comments, and useful and thoughtful suggestions. I would like to offer my deepest thank and appreciation and give full credit to Eric Burgett, fellow doctoral candidate at Georgia Institute of Technology, and Ian Gifford, fellow doctoral candidate here at the University of Maryland, for performing the difficult neutron spectrum unfolding at the thermal column and providing me with the unfolded data. I would like specially thank my fellow doctoral candidate Colonel Donald Hall for his insight and without his suggestions, some issues, especially burnup, could not have been resolved in time. I would like specially to thank Vincent Adams for always being thoughtful and for answering my difficult questions about the Maryland reactor, and providing iii me with the necessary experimental data; without his help, this work wouldn’t be complete. iv Table of Contents Dedication.....................................................................................................................ii Acknowledgements......................................................................................................iii Table of Contents..........................................................................................................v List of Tables..............................................................................................................vii List of Figures............................................................................................................viii Chapter 1 : Introduction................................................................................................1 1.1 Objective and Research Needs......................................................................1 1.2 Literature Review..........................................................................................2 Chapter 2 : Nuclear Reactor Theory.............................................................................5 2.1 Neutron Transport and Reactor Theory........................................................5 2.2 The Neutron Transport Equation..................................................................5 2.3 Approximation to the Neutron Transport Equation......................................7 2.4 The P Approximation and Diffusion Theory..............................................8 N 2.5 The Discrete Ordinate Method......................................................................9 2.6 The Monte Carlo Method............................................................................11 2.7 The Physics of TRIGA Reactors.................................................................17 Chapter 3 : Reactor Model Development...................................................................21 3.1 Description of MUTR.................................................................................21 3.2 The MCNP/MCNPX Code.........................................................................22 3.3 Description of the MCNP/MCNPX Model.................................................23 3.3.1 Outline of MCNP Model description..................................................23 3.3.2 Standard TRIGA Fuel Element Description.......................................25 3.3.3 Four-Rod Fuel Cluster Description.....................................................29 3.3.4 MCNP Model of the Four-Rod Fuel Cluster......................................30 3.3.5 Control Rods.......................................................................................33 3.3.6 Control Rod Fuel Cluster....................................................................33 3.3.7 MCNP Model of Control Rod Fuel Cluster........................................33 3.3.8 The Pneumatic Transfer System—the Rabbit.....................................35 3.3.9 Neutron Moderator and Reflector.......................................................36 3.3.10 The Thermal Column..........................................................................37 3.4 MCNP Geometry Model of MUTR............................................................38 3.5 Materials Used in the MCNP Model..........................................................41 3.6 MCNP Criticality Calculation Setup..........................................................43 3.6.1 Structure of the MCNP Input File.......................................................43 3.6.2 Setup of the MCNP Criticality Calculations......................................45 3.7 Precision of the Monte Carlo Calculations.................................................46 3.8 Variance Reduction.....................................................................................46 3.9 Analog and Non Analog Monte Carlo Sampling........................................47 3.10 Validity of the Monte Carlo Precision........................................................49 Chapter 4 : Results and Discussion.............................................................................50 v 4.1 Summary of the Results..............................................................................50 4.2 Reactor Core Criticality Calculations.........................................................52 4.3 Calculation of the Neutron Flux Spectrum at the Thermal Column...........54 4.4 Weight Windows........................................................................................55 4.5 The Thermal Column Flux Calculation Optimization................................57 4.6 Results of the thermal Column Calculations..............................................59 4.7 Neutron Spectrum Unfolding Measurements.............................................63 4.8 Results and Analysis of Core Geometry Approximations..........................66 4.8.1 Survey of TRIGA Fuels......................................................................70 4.8.2 Graphite Reflectors Neutronic Effects................................................71 4.9 Results of Uncertainty Calculations............................................................74 4.10 Fuel Burnup Effect......................................................................................75 4.11 Short Term Reactivity Effects—Fission Products Poisoning.....................75 4.12 Long Term Reactivity Effects.....................................................................76 4.13 MCNPX Burnup Process............................................................................78 4.14 Results of Flux Calculations in The Rabbit System...................................79 4.15 Study of Fuel Burnup Using Cell Calculations..........................................81 Chapter 5 : Conclusions and Recommendations.......................................................83 Appendix A.................................................................................................................85 A.1 MCNP Model of the Detailed MUTR Core................................................85 A.2 MCNP Model of the Simplified Core of MUTR......................................104 A.3 MCNP Model of MUTR Pin Cell (Unit Cell)..........................................119 Bibliography.............................................................................................................122 vi List of Tables Table 3.1: Materials Composition used in MCNP Model of MUTR.........................41 Table 4.1: Comparison of Experimental and MCNP Calculated Flux Data...............51 Table 4.2: Neutron Flux-to-Dose Rate Conversion Factors [6]..................................62 Table 4.3. Thermal Neutron Activation Reactions.....................................................66 Table 4.4: Scattering and Absorption Cross Sections For Water and Aluminum []...68 Table 4.5 :Multiplication factor benchmarks during initial reactor startup................68 Table 4.6: Standard TRIGA Fuel Element Dimensions.............................................71 Table 4.7: Change of keff with Graphite Reflector Thickness...................................72 Table 4.8: Flux for Graphite Reflectors with at Different Lengths............................73 Table 4.9: Three-parameter Uncertainty Matrix.........................................................74 Table 4.10: Thermal Cross Sections Data (0.0253 eV) for Fissile and Fertile Nuclides [, , ]..............................................................................................................................78 vii