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Fluoride-Salt-Cooled High-Temperature Test Reactor Fluoride-Salt-Cooled High-Temperature Test Reactor Thermal-Hydraulic Licensing and Uncertainty Propagation Analysis by Rebecca Rose Romatoski Submitted to the Department of Nuclear Science and Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Nuclear Science and Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2017 c Massachusetts Institute of Technology 2017. All rights reserved. Author............................................................................ Department of Nuclear Science and Engineering May 2, 2017 Certified by........................................................................ Dr. Lin-wen Hu Director of Research and Services, Principal Research Scientist, Nuclear Reactor Lab Thesis Supervisor Certified by........................................................................ Professor Jacopo Buongiorno TEPCO Professor and Associate Department Head, Nuclear Science and Engineering Director, Center for Advanced Nuclear Energy Systems Thesis Reader Certified by........................................................................ Dr. Charles Forsberg Principal Research Scientist of Nuclear Science and Engineering Thesis Reader Accepted by....................................................................... Professor Ju Li Battelle Energy Alliance Professor of Nuclear Science and Engineering Professor of Materials Science and Engineering Chair, Department Committee on Graduate Students 2 Fluoride-Salt-Cooled High-Temperature Test Reactor Thermal-Hydraulic Licensing and Uncertainty Propagation Analysis by Rebecca Rose Romatoski Submitted to the Department of Nuclear Science and Engineering on May 2, 2017, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Nuclear Science and Engineering Abstract An important Fluoride-salt-cooled High-temperature Reactor (FHR) development step is to design, build, and operate a test reactor. Through a literature review, liquid-salt coolant thermophysical properties have been recommended along with their uncertainties of 2- 20%. This study tackles determining the effects of these high uncertainties by propos- ing a newly developed methodology to incorporate uncertainty propagation in a thermal- hydraulic safety analysis for test reactor licensing. A hot channel model, Monte Carlo statistical sampling uncertainty propagation, and limiting safety systems settings (LSSS) approach are uniquely combined to ensure sufficient margin to fuel and material thermal limits during steady-state operation and to incorporate margin for high uncertainty inputs. The method calculates LSSS parameters to define safe operation. The methodology has been applied to two test reactors currently considered, the Chinese TMSR-SF1 pebble bed design and MIT's Transportable FHR prismatic core design; two candidate coolants, flibe (LiF-BeF2) and nafzirf (NaF-ZrF4); and forced flow and natural circulation conditions to compare operating regions and LSSS power (maximum power not exceeding any thermal limits). The calculated operating region accounts for uncertainty (2σ) with LSSS power (MW) for forced flow of 25.37±0.72, 22.56±1.15, 21.28±1.48, and 11.32±1.35 for pebble flibe, pebble nafzirf, prismatic flibe, and prismatic nafzirf, respec- tively. The pebble bed has superior heat transfer with an operating region reduced ∼10% less when switching coolants and ∼50% smaller uncertainty than the prismatic. The maxi- mum fuel temperature constrains the pebble bed while the maximum coolant temperature constrains the prismatic due to different dominant heat transfer modes. Sensitivity anal- ysis revealed 1) thermal conductivity and thus conductive heat transfer dominates in the prismatic design while convection is superior in the pebble bed, and 2) the impact of ther- mophysical property uncertainties are ranked in the following order: thermal conductivity, heat capacity, density, and lastly viscosity. Broadly, the methodology developed incorporates uncertainty propagation that can be used to evaluate parametric uncertainties to satisfy guidelines for non-power reactor li- censing applications, and method application shows the pebble bed is more attractive for thermal-hydraulic safety. Although the method was developed and evaluated for coolant property uncertainties for FHR, it is readily applicable for any parameters of interest. Thesis Supervisor: Dr. Lin-wen Hu Title: Director of Research and Services, Principal Research Scientist, Nuclear Reactor Lab 3 4 Acknowledgments I gratefully acknowledge the guidance, support, and encouragement of my doctoral supervi- sor, Dr. Lin-wen Hu, and the members of my committee: Dr. Charles Forsberg, Professor Mike Short, Professor Jacopo Buongiorno, and Professor Ben Forget, as well as the folks at the Nuclear Reactor Laboratory and the Nuclear Science and Engineering Communication Lab. My gratitude extends to the wonderful administrators of the Nuclear Science and Engi- neering department especially Lisa, Rachel, and Rachel and to all my friends across campus from the Women's Ice Hockey Club Team, Fossil Free MIT, the Graduate Student Council, the Women in NSE, Burton Conner house team and all the students on Burton 5. This dissertation would not have been possible without funding from the Department of Energy Nuclear Engineering University Program and Shanghai Institute of Applied Physics Chinese Academy of Sciences. A special thanks to my family, especially my spouse Bobby. Life is always good with you in it. Much love to my Mom, Dad, brother Zach, and sister Kelsey. Also, to my in-laws and all my extended family. Lastly, Zinn you are the sweetest little boy. I'm so glad you got to see your Mama defend her dissertation!! 5 6 Contents 1 Introduction 21 1.1 Background and Motivation . 21 1.2 Objectives . 26 1.2.1 Understanding Uncertainties . 26 1.2.2 Thermal Hydraulic Licensing Approach . 26 1.2.3 Comparison of FHTR Designs . 27 2 Reactor Concept 29 2.1 Technology Features . 31 2.1.1 TRISO Particle Fuel . 31 2.1.2 High-Temperature Coolant . 38 2.1.3 Passive Safety . 40 2.1.4 Power Cycle Economics . 42 2.2 Test Reactor Designs . 45 2.2.1 Pebble Bed Core . 45 2.2.2 Prismatic Core . 49 3 Liquid Salt Coolant Properties and Heat Transfer Coefficient 53 3.1 Salts Selected . 55 3.2 Ideal Behavior of Thermophysical Properties . 56 3.2.1 Density . 56 3.2.2 Heat Capacity . 56 3.2.3 Thermal Conductivity . 57 3.2.4 Viscosity . 60 3.3 Literature Review of Selected Salt Properties . 61 7 3.3.1 Data Sources . 61 3.3.2 Flibe . 69 3.3.3 Nafzirf . 84 3.3.4 Flinak . 91 3.4 Recommended Thermophysical Properties . 98 3.5 Heat Transfer Coefficient of Molten Salts . 100 3.5.1 General Heat Transfer Correlations . 100 3.5.2 Molten Salt Heat Transfer Correlations . 105 3.5.3 Simulation of Salt Heat Transfer Correlations . 112 3.5.4 Recommended HTC Correlations . 115 4 Test Reactor Licensing 117 4.1 Test Reactor Goals . 119 4.2 Test Reactor Classification and Ownership . 121 4.3 Licensor . 123 4.4 Limiting Safety Systems Settings . 125 4.5 LSSS Thermal Limits . 127 4.5.1 Coolant Temperature . 127 4.5.2 Structural Material Temperature . 128 4.5.3 Fuel Temperature . 130 4.5.4 LSSS Criteria . 130 4.6 LSSS Operating Region . 132 5 Hot Channel Model 135 5.1 Total Hot Channel Factors . 137 5.2 Combining Factors . 138 5.3 Nuclear Hot Channel Power Peaking Factors . 139 5.4 Engineering Hot Channel Factors . 140 5.5 Implementation of Hot Channel Factors . 143 5.6 Hot Channel Factor Calculations . 146 5.6.1 Nuclear Hot Channel Power Peaking Factors . 146 5.6.2 Engineering Hot Channel Factors . 146 5.6.3 Flow Factors . 153 8 5.7 FHR Hot Channel Factor Summary . 155 6 Uncertainty 157 6.1 Determining Uncertainty . 158 6.1.1 Statistical Distributions . 159 6.1.2 Random Sampling . 161 6.1.3 Systematic Uncertainty . 165 6.1.4 Overall Uncertainty . 166 6.2 Uncertainty Propagation . 167 6.2.1 Taylor Series Method . 167 6.2.2 Monte Carlo Sampling Method . 169 6.2.3 Perturbation Method . 169 6.2.4 Moment Equations . 171 6.2.5 Bayesian Inverse Approach . 172 6.3 Approach to Uncertainty . 174 6.3.1 Hot Channel Model . 174 6.3.2 Sensitivity Study . 174 6.3.3 Monte Carlo Uncertainty Quanification . 175 7 Thermal-hydraulic Uncertainty Propagation Licensing Analysis 179 7.1 Single Input Point Analysis . 182 7.1.1 Coolant Temperature and Flow . 182 7.1.2 Convective Heat Transfer . 186 7.1.3 Conduction in Fuel Elements . 189 7.1.4 Radiation Heat Transfer . 196 7.1.5 TUPLA Inputs and Outputs . 197 7.2 Single LSSS Analysis . 200 7.2.1 Forced Flow . 200 7.2.2 Natural Circulation Flow . 201 7.3 LSSS Sensitivity Study and Uncertainty Quantification Analyses . 202 8 Results and Discussion 203 8.1 Code to Code Comparison . 205 9 8.1.1 Code to Code Agreement . 205 8.1.2 Code Performance . 208 8.2 Axial Nodal Reactor Temperature Profiles . 210 8.3 LSSS Results . 215 8.3.1 Comparison of Reactor Designs . 215 8.3.2 Most Limiting Constraint . 220 8.3.3 Comparison to Water Reactors . 220 8.4 LSSS Sensitivity Study . 223 8.4.1 Sensitivity of Thermophysical Coolant Properties . 223 8.4.2 Sensitivity of Heat Transfer and Flow Parameters . 225 8.5 LSSS Uncertainty Propagation . 230 8.5.1 Comparison of Reactor Designs . 236 8.5.2 Comparison of Coolants . 236 9 Summary and Conclusions 239 9.1 Project Summary . 239 9.2 Results Summary . 242 9.3 Test Reactor.
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