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Modeling and Simulation of the Transient Reactor Test Facility Using Modern Neutron Transport Methods by Travis J

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Modeling and Simulation of the Transient Reactor Test Facility Using Modern Neutron Transport Methods by Travis J Modeling and Simulation of the Transient Reactor Test Facility using Modern Neutron Transport Methods by Travis J. Labossi`ere-Hickman B.S., University of Tennessee, Knoxville (2016) Submitted to the Department of Nuclear Science & Engineering in partial fulfillment of the requirements for the degree of Master of Science in Nuclear Science & Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2019 ○c Massachusetts Institute of Technology 2019. All rights reserved. Author................................................................ Department of Nuclear Science & Engineering May 10, 2019 Certified by. Benoit Forget Professor of Nuclear Science & Engineering Thesis Supervisor Certified by. Kord Smith KEPCO Professor of the Practice of Nuclear Science & Engineering Thesis Supervisor Accepted by . Ju Li Battelle Energy Alliance Professor of Nuclear Science & Engineering and Professor of Materials Science & Engineering Chair, Department Committee on Graduate Students 2 Modeling and Simulation of the Transient Reactor Test Facility using Modern Neutron Transport Methods by Travis J. Labossi`ere-Hickman Submitted to the Department of Nuclear Science & Engineering on May 10, 2019, in partial fulfillment of the requirements for the degree of Master of Science in Nuclear Science & Engineering Abstract The Transient Reactor Test Facility (TREAT) has regained the interest of the nuclear engineering community in recent years. While TREAT’s design makes it uniquely suited to transient fuel testing, it also makes the reactor very challenging to model and simulate. In this thesis, we build a Monte Carlo model of TREAT’s Minimum Critical Mass core to examine the effects of fuel impurities, calculate a reference solution, and analyze a number of multigroup cross section generation approaches. Several method of characteristics (MOC) simulations employing these cross sections are then converged in space and angle, corrected for homogenization, and compared to the Monte Carlo reference solution. The thesis concludes with recommendations for future analysis of TREAT using MOC. Thesis Supervisor: Benoit Forget Title: Professor of Nuclear Science & Engineering Thesis Supervisor: Kord Smith Title: KEPCO Professor of the Practice of Nuclear Science & Engineering 3 4 Acknowledgments This work would not have been possible without the support of the MIT CRPG. I would especially like to thank Will Boyd, Sterling Harper, and Guillaume Giudicelli for instructing me in the ways of OpenMC and OpenMOC; Carl Haugen for co- building the full TREAT reactor model; Zhaoyuan Liu for providing the Cumulative Migration Method data; and Professors Benoit Forget and Kord Smith for their advising and for putting up with me these past few years. I would like to thank the American Nuclear Society for providing me with the opportunities which led to discovering the CRPG and for finding my first job at Framatome. I also wish to express my gratitude to my brothers and sisters of the MIT Graduate Christian Fellowship for their edification and for reminding me what was really important. This material is based upon work supported under an Integrated University Pro- gram Graduate Fellowship. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the Department of Energy Office of Nuclear Energy. This research made use of the resources of the High Performance Computing Center at Idaho National Laboratory, which is supported by the Office of Nuclear Energy of the U.S. Department of Energy and the Nuclear Science User Facilities under Contract No. DE-AC07-05ID14517. 5 6 Contents 1 Introduction 19 2 Background 21 2.1 Construction of TREAT......................... 21 2.2 Core.................................... 21 2.2.1 Standard Fuel Assembly..................... 23 2.2.2 Control Rod Fuel Assembly................... 24 2.2.3 Control rods............................ 25 2.2.4 Dummy Assemblies........................ 25 2.3 Fuel of TREAT.............................. 25 2.3.1 Boron Impurity.......................... 26 2.3.2 Hydrogen Impurity........................ 27 2.3.3 Graphitization Fraction..................... 27 2.4 Computational Methods......................... 28 2.4.1 Monte Carlo............................ 28 2.4.2 MGXS............................... 28 2.4.3 MOC................................ 29 2.5 Equivalence Methods........................... 31 2.5.1 Cumulative Migration Method.................. 31 2.5.2 Superhomog´en´eisation...................... 33 3 TREAT Reference Solutions 35 3.1 Minimum Critical Mass Model...................... 35 7 3.2 Fuel Composition............................. 36 3.2.1 Base Model............................ 36 3.2.2 Sensitivity to Boron....................... 37 3.2.3 Sensitivity to Hydrogen..................... 37 3.2.4 Sensitivity to Graphitization................... 38 3.3 Simplified OpenMC Models for OpenMOC Analysis............................ 38 3.3.1 Single Standard Fuel Element.................. 39 3.3.2 3×3 Colorset (Follower)..................... 40 3.3.3 3×3 Colorset (Poison)...................... 40 3.3.4 MCM2D (No Rods)........................ 41 3.3.5 MCM2D (Follower)........................ 41 3.3.6 MCM2D (Poison)......................... 42 3.4 MGXS Generation: Energy Groups................... 42 3.5 MGXS Generation: Spatial Domains.................. 44 3.5.1 Mesh Domain........................... 44 3.5.2 Material Domain......................... 47 3.5.3 Cell Domain............................ 48 3.5.4 Universe Domain......................... 49 3.5.5 Heterogeneous vs. Homogeneous Representation........ 49 4 Deterministic Results 51 4.1 Variables to Converge........................... 51 4.2 Source Region Convergence....................... 52 4.2.1 CMFD Convergence....................... 53 4.2.2 1D Convergence Study...................... 54 4.2.3 2D Colorset Convergence..................... 56 4.2.4 2D Full-Core Convergence.................... 64 4.3 Ray Spacing and Azimuthal Angle Convergence............ 74 4.3.1 Heterogeneous........................... 74 8 4.3.2 Homogeneous........................... 76 4.4 Polar Angle Convergence......................... 76 4.5 Effects of Corrections for Homogeneous Models............ 77 4.5.1 Correcting with CMM...................... 77 4.5.2 Correcting with SPH....................... 86 4.6 Final Results............................... 92 4.6.1 Single Fuel Element Results................... 92 4.6.2 3×3 Colorset (Follower) Results................. 93 4.6.3 3×3 Colorset (Poison) Results.................. 94 4.6.4 MCM2D (No Rods) Results................... 95 4.6.5 MCM2D (Follower) Results................... 96 4.6.6 MCM2D (Poison) Results.................... 97 5 Conclusions 99 5.1 Summary of Accomplishments...................... 99 5.2 Recommendations for Future Analysts................. 100 A Enlarged Figures 103 B CMM Transport Correction Ratios 107 C Software Versions 109 C.1 OpenMC.................................. 109 C.1.1 Revision used for sensitivity analysis.............. 109 C.1.2 Revision used for MGXS generation............... 109 C.2 OpenMOC................................. 110 9 10 List of Figures 2.1 Top view of the TREAT core...................... 22 2.2 Minimum Critical Mass core configuration............... 22 2.3 Axial cutaway of a standard fuel element................ 23 2.4 Axial cutaway of a control rod fuel element............... 24 2.5 Regions of a TREAT control rod.................... 25 2.6 Axial cutaway of an aluminum-clad dummy element.......... 26 2.7 Construction of a CSG cell from basic surfaces............. 29 2.8 Example of flat vs. linear source regions for a 1D gradient...... 30 3.1 Full-reactor MCM model at midcore.................. 35 3.2 Legend for the subsequent materials plots............... 39 3.3 Single standard fuel element....................... 39 3.4 3×3 control rod colorset (graphite follower inserted).......... 40 3.5 3×3 control rod colorset (B4C poison inserted)............. 40 3.6 MCM full core (no control rod elements)................ 41 3.7 MCM full core (graphite follower inserted)............... 41 3.8 MCM full core (B4C poison inserted).................. 42 3.9 Fine mesh over a single fuel element................... 44 3.10 1D XS plots with error bars....................... 45 3.11 Fine mesh over a control rod (follower) fuel element........... 45 3.12 Mesh tally across the MCM2D (Poison) core.............. 46 3.13 Thermal fission mesh tally across the MCM2D (Poison) core..... 47 3.14 Control rod (follower) fuel element, Material domain.......... 47 11 3.15 Control rod (follower) fuel element, Cell domain............. 48 3.16 Control rod (follower) fuel element, Universe domain.......... 49 3.17 Heterogeneous vs. Homogeneous representations of MCM2D Poison. 50 4.1 Azimuthal rings and sectors for a pincell in a box........... 52 4.2 Subdivision of a TREAT element.................... 53 4.3 Geometry of toy problem......................... 54 4.4 Flat source vs. linear source for toy problem.............. 55 4.5 Converged LSR meshes for the single fuel element........... 57 4.6 Converged LSR meshes for the 3×3 colorset (follower)......... 59 4.7 Converged LSR meshes for the 3×3 colorset (poison)......... 62 4.8 Power distributions for the 3×3 colorset (poison) models....... 63 4.9 Converged LSR meshes for the MCFuel core.............. 65 4.10 MCM2D (No Rods): 11 groups vs. 25 groups............. 66 4.11 MCM2D (Follower):
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